Measurement of total hemispherical emissivity ... - thermophysics.ru

MEASUREMENT OF TOTAL HEMISPHERICAL EMISSIVITY USING ACALORIMETRIC TECHNIQUEJ Hameury, B Hay, J-R FiltzLaboratoire National de Métrologie et d'Essais (LNE), 29 Avenue Roger Hennequin,78197 TRAPPES Cedex, France, Email : jacques.hameury@lne.frABSTRACTAn apparatus has been designed by LNE (Laboratoire National d'Essais) to measure, using acalorimetric technique, the total hemispherical emissivity of opaque solid materials, in thetemperature range –20 to 200°C.Two samples of the material are heated at a steady temperature by an electrical resistor. Thesamples are surrounded by guard-rings, heated at the same temperature as the samples, inorder to ensure that the heat flows in the samples are unidirectional and axial. The system isplaced in a large vacuum chamber with internal walls coated with a high emissivity blackpaint. The walls are thermostated at 78 K by liquid nitrogen. Thus the electrical powersupplied to the resistor is almost totally dissipated by radiation by the two plane circularsurfaces of the samples facing the chamber walls. Two thermocouples are radially embeddedin each sample at two different distances from the surface. The surface temperature of eachsample is extrapolated using a simple linear model. The mean total hemispherical emissivityof the two samples is calculated using a radiative model that considers the main surfacesradiating in the chamber. To achieve good accuracy, edge heat losses and heat losses thoughthe gas remaining in the chamber are evaluated and corrected.Facility design, model of calculation, evaluation of corrections and uncertainties assessmentare described. The technique of measurement was validated by comparison with a radiativetechnique of measurement used at PTB (Physikalisch Technische Bundesanstalt) in Germany.The expanded uncertainty (k = 2) on the total hemispherical emissivity is estimated lowerthan ± 0.03 for materials with high emissivity and conductivity higher than 1W m -1 K -1 .KEY WORDS : Total hemispherical emissivity, solid materials, heat losses corrections,uncertainty analysis.1

2.1. Heating systemFigure 2 shows a cross-section of the heating system with the two samples and the thermalguard.For convenience, the following vocabulary is used:- meter plate : the system used to heat the samples, made of an electrical heater (disc) and oftwo copper discs to have a uniform temperature,- guard ring : the system used to heat the "samples rings", made of an electrical heater (ring)and of two copper rings,- samples rings : the two rings, heated by the guard ring, that surround the samples.This vocabulary is the same (or very closed) to the one used by people doing thermalconductivity measurements with guarded hot plates [4], [5].Two heaters are used, one for the two samples and the other one for the two samples rings.The electrical heaters are thin flexible heating elements consisting of a foil resistive elementlaminated between layers of polyimide film ; the limit temperature of the heaters is 210°C.The sample heater (disc shape) is sandwiched between 2 copper discs (diameter = 62.2 mm,thickness = 5mm) and the guard ring heater (ring shape) is sandwiched between 2 copperrings (inner diameter = 64.2 mm, outer diameter = 120.7 mm). The gap between the meterplate and the guard ring (Figure 3) is 1 mm wide except the opening, which is 0.1 mm wide.On each side of the heating system, the copper disc is attached to the ring by four bindingsmade of structural epoxy (section 5 mm × 5 mm). The guard ring temperature is controlled byan eight stages thermopile across the gap. Four stages of the thermopile are embedded in thecopper disc and the copper ring of each side of the heating plate. The thermopile wires areembedded in grooves filled with epoxy resin with a "high" thermal conductivity(1.8 W m -1 K -1 ). The temperature of the meter plate is controlled by a chromel/alumelthermocouple embedded in a copper disc.Axis61781095432Fig. 2. Cross section of the heating system with samples and rings : (1) samples; (2) samplesheating resistor; (3) copper discs; (4) guard ring heating resistor; (5) copper rings; (6) samplesrings; (7) thermopile, (8) thermocouples; (9) wires guard block; (10) wires.3

Revolutionaxis0,1 mm1,5 mmSampleSampleSample ringring10 mmCopper disk of the meter plateCopper ring of theguard ring5 mm1 mmFig. 3. Expanded view of the gap.2.2. SamplesTwo identical samples are needed for a measurement. The shape and dimensions of thesamples are shown by Figure 4 . Two radial holes (diameter 1.2 mm) are drilled in eachsample at known distances from the surface. If the material, to be characterized in emissivity,is thin then two samples of the material are stuck on two metallic discs with one or two holesfor thermocouples. If the material is a coating (paint, varnish, …) then the coating is appliedto two metallic discs.8.0 mm2.0 mmA - A∅ 62.2 mmA1 hole ∅ 1.2 mmdepth 15 mmSurface to becaracterized inemissivity90°1 hole ∅ 1.2 mmdepth 15 mm10 mmAFig. 4. Samples.4

2.3. Samples ringsEach sample is surrounded by a ring (called "sample ring") heated by the guard ring. Ideally,the samples rings would be made of the same material as the samples, in order to have thesame distribution of temperature as the sample (same gradient). In fact for convenience, threesets of samples rings can be used, one made of stainless steel, one made of aluminium alloyand one made of copper. The samples rings are fasten to the guard ring with screws. Threesmall clamps attached to each sample ring are used to press each sample on the meter plate.2.4. WIRES GUARD BLOCKA thermal guard (called "wires guard block") is used to heat all the wires that connect theheating system to the measuring devices or the electrical supplies (thermocouples, thermopile,electrical supplies). A similar system is described in [1] for an emissometer and in [5] for aguarded hot plate used for thermal conductivity measurement. The "wires guard block" isused to avoid an important local perturbation of the temperature distribution in the guard ring.The temperature of the block is controlled by a differential thermocouple between the blockand the guard ring.2.5. VACUUM CHAMBERThe chamber, made of stainless steel, has an internal surface of 1.36 m². The surface is coatedwith the Nextel Velvet Coating 811-21 black paint. The total hemispherical emissivity of thepaint, measured by PTB (Physikalisch Technische Bundesanstalt), is 0.943 at –60°C [6]. Awell (diameter 200 mm) is used to insert the heating system inside the chamber. The wall ofthe well is electro-polished to reduce the emissivity. A stacking of three screens, made ofpolished aluminium, is used to reduce the direct radiation flux, coming from the upper andhotter part of the well, inside the chamber. The gases are pumped out through an openingbetween the screens and the tube.2.6. VACUUM PUMPING SYSTEMThe pumping system is made of a turbomolecular pump associated with a rotary vane pumps.The gas in the chamber is pumped out, while the chamber is at ambient temperature, until thepressure reaches 5 10 -3 Pa. Then the liquid nitrogen is transferred into the dewar and thepressure in the chamber falls to less than 10 -3 Pa.5

2.7. INSTRUMENTATION AND CONTROL DEVICESThe temperatures in the heating plate (meter plate and guard ring), in the two samples and inthe samples rings are measured with chromel/alumel thermocouples connected to a highprecision calibrated voltmeter.The temperatures of the meter plate and the one of the guard ring are controlled by a dual loopEurotherm controller with a high resolution. Each loop of the controller pilots a DC powersupply.The intensity supplied to the meter plate is measured indirectly by measuring the voltage atthe terminals of a calibrated shunt resistor and the voltage is measured directly at theterminals of the heater (inside the meter plate).The pressure in the chamber is controlled with a Penning manometer.3. EMISSIVITY CALCULATION3.1. EMISSIVITY CALCULATIONThe total hemispherical emissivity is computed from the net heat-transfer rate of the circularsurfaces of the samples. Many models, more or less complex, can be built up to relate theemissivity to the electrical power supplied to the meter plate, to the surface temperature of thesamples and to the temperatures of the surfaces present in the surroundings of the samples.The complexity of the model depends on the number of surfaces that are considered. Most ofthe models found in literature are very simple, for example the emissivity of the chamberwalls is considered to be equal to one, like in [7] and [2], or the number of elements isreduced to the samples and the chamber walls [1].Our model is quite simple and considers 3 surfaces : the circular radiating surfaces of the twosamples, the surfaces of the rings (plane annular surfaces and cylindrical surfaces), thechamber walls. The model is built up using the "radiosity method", that is to say consideringthat the emission of the surfaces is Lambertian, the reflection on the surfaces is perfectlydiffuse and the spectral emissivities of the surfaces are independent of wavelengths.The heat balance equation for the two samples gives the relation :( P ) ⎛⎞elec.− PleaksSr⎜ ε ( )⎟c+ εr1−εcSs⎝ Scε⎠s=(1)4 ⎛ S ⎞⎛( )( − ) ⎞r⎜ + −⎟ −4Sr4 Pelec.Pleaksσ T− −⎜+⎟sεcεr1 εcεcσ Tc(1 εc) εrσ Tr⎝ Sc⎠⎝ ScSc⎠where : ε sis the total hemispherical emissivity of the samples, Pelec.is the electrical powersupplied to the meter plate, P leaksis the thermal power "lost" by the samples and the meterplate by other ways than radiation by the two circular surfaces of the samples, Ssis the sumof the two circular surfaces of the samples, ε cis the total hemispherical emissivity of the6

chamber walls, εris the mean total hemispherical emissivity of the rings surfaces, Sris thesurface of the samples rings radiating toward the chamber walls, S cis the surface of thechamber walls, σ is the Stefan-Boltzman constant, Tsis the mean surface temperature of thetwo samples, T cis the mean temperature of the chamber walls, T ris the mean surfacetemperature of the two rings.Pleaksis considered positive when the heat is lost by the samples or by the meter plate andnegative when the heat is received.The real surface temperatures of the two samples are slightly different, thus the mean surfacetemperature used to calculate the emissivity is calculated using the relation :1444⎛ S⎞s1Ts1+ Ss2Ts2T s=⎜⎟(2)⎝ Ss1+ Ss2⎠where : Tsis the mean surface temperature of the two samples, Ss1is the size of the circularsurface of sample no. 1, S s2is the size of the circular surface of sample no. 2, T s1is thesurface temperature measured for the sample no. 1, T s2is the surface temperature measuredfor the sample no. 2.3.2. UNCERTAINTY OF THE MODELThe uncertainty of the model has been evaluated by comparison to a model considering fivesurfaces. The "true" value of the power radiated by the samples is supposed to be the onegiven by the five surfaces model (chamber walls, samples, rings, screens around the rings,screens and opening of the well). The relative difference between the emissivity calculatedwith the 3 surfaces model and the "true" emissivity is lower than 0.11%.3.3. HEAT LOSSES EVALUATIONThe parasitic heat fluxes lost or gained by the samples and the meter plate are :- the radiation flux lost by the edge of the samples (cylindrical surface),- the radiation flux lost by the edge of the meter plate (copper discs),- the conduction flux between each sample and the corresponding sample ring,- the flux lost by conduction or convection though the gas remaining in the chamber.3.2.1. EDGE LOSSES BY RADIATIONThe geometry of the gap is shown by Figure 3. A radiosity model was built up to calculate theradiative net heat flux lost by the sample edge (cylindrical surface). Due to the symmetry ofthe system, the calculation was done only for one side of the heating system. In the modeleach surface is supposed to be isothermal. So the calculation was done considering the meantemperature at half thickness of the sample and of the sample ring. The mean temperatures arecalculated from the measured temperatures.7

The results show that, if the mean temperature of the sample is the same as the one of thesample ring, the gap radiates toward the chamber like a black body at the mean temperature ofthe sample. This is not surprising because of the low value of the ratio surface of the openingof the gap to internal surface. Thus, if the mean temperature of the sample is the same as theone of the sample ring, the heat flux lost by radiation by the edge of the sample depends onlyon the ratio emissivity of the sample edge to emissivity of the edge of the sample ring;Figure 5 shows that evolution. If the mean temperatures of the sample and of the ring are thesame and if the emissivities of the sample edge is the same as the one of the edge of the ring,then the heat flux lost by radiation by the sample edge is equivalent to an emissivity of 0.0032for the circular surface of the sample.0.8Ratio : ( heat flux lost by radiation /measured heat flux) * 1000.70.60.50.40.30.20.10Emissivity of the circular surface of the sample =0.90 1 2 3 4 5 6 7 8 9 10 11 12Ratio : Emissivity of the cylindrical surface of the sample / emissivity of the cylindrical surfaceof the ringFig. 5. Radiative heat flux lost by the edge of the sample3.2.2. EDGE LOSSES BY CONDUCTIONA difference of temperature between each sample and the corresponding sample ring canoccur if the thermal contact resistance between the sample ring and the guard ring is differentthan the one between the sample and the meter plate. The temperature of each ring ismeasured using two thermocouples (like for samples). The value evaluated for the heattransfer coefficient by conduction through the four thermocouples embedded in the samples is0.11 W/K.The heat flux by conduction between the meter plate and the guard ring is supposed to benegligible because the temperature of the guard ring is controlled to be almost the same as theone of the meter plate. Nevertheless, a term of uncertainty is considered for that heat flux.8

3.2.3. HEAT LOSS BY THE GAS REMAINING IN THE CHAMBERDuring emissivity measurements the gas remaining in the chamber is at a pressurebelow 10 -3 Pa. The longer distance between the sample and a point of the chamber walls isabout 300 mm. At a pressure below 10 -2 Pa, the mean free path for a molecule of air is longerthan 0.64 m [8], that is to say the mean free path is longer than the greatest dimension of thechamber. Thus the equivalent thermal conductivity of air is proportional to pressure (kineticgas theory [8]).The flux lost by the circular surface of a sample is given by the relation [8]:Φair= K Ssamplesa P ( Tsample−Twalls)(3)where : K is a characteristic of the gas (K= 1.2 for nitrogen), S samplesis the surface of thesample, a is the accommodation coefficient ( a = 1 for air at 77 K), P is the pressure of thegas, Tsampleis the surface temperature of the sample and T wallsis the temperature of thechamber walls.Measurement of variations of the power supplied to the meter plate versus pressure in thechamber were made, the results are given in Table I. The measurements were made with lowemissivity samples ( ε = 0. 055 ) at 100°C. The power varies linearly with the pressure for apressure below 2 10 -2 Pa (molecular regime). The heat transfer coefficient was calculatedconsidering that the power measured at 2 10 -4 Pa is the same as the one without any moleculeof gas. The theoretical heat transfer coefficient given by Eq. (3) is also given in Table I. Themeasured heat transfer coefficient is of the same order than the one given by the theory for apressure below 2 10 -2 Pa (molecular regime).Table II give the emissivity equivalent to the power transferred by the remaining gas fordifferent temperatures. A fairly good vacuum is needed to have a negligible error due to heattransfer by air, a pressure lower than 10 -3 Pa induces a negligible error for all the temperaturerange.9

PressurePowerHeat transfer coefficientthrough the gasHeat transfer coefficientcalculated using Eq. (3)(Pa)(W)(W/(m² °C))(W/(m² °C))2.00 × 10 -4 0.366 - 2.40 × 10 -45.00 × 10 -4 0.367 5.60 × 10 -4 6.00 × 10 -42.00 × 10 -3 0.37 2.20 × 10 -3 2.40 × 10 -35.00 × 10 -3 0.375 5.00 × 10 -3 6.00 × 10 -32.00 × 10 -2 0.406 2.20 × 10 -2 2.40 × 10 -25.00 × 10 -2 0.435 3.80 × 10 -2 6.00 × 10 -22.00 × 10 -1 0.491 6.90 × 10 -2 2.40 × 10 -1Table I.Power supplied to the meter plate versus pressure,Heat transfer coefficient through the gas.PressureEmissivity equivalent to the heat loss through the gasSurface temperature(Pa) -20 °C 20 °C 100 °C 200 °C1.0 × 10 -4 0.0001 0.0001 0.0000 0.00005.0 × 10 -4 0.0005 0.0003 0.0002 0.00011.0 × 10 -3 0.0009 0.0006 0.0003 0.00025.0 × 10 -3 0.0046 0.0031 0.0016 0.00081.0 × 10 -2 0.0092 0.0062 0.0032 0.00172.0 × 10 -2 0.0183 0.0125 0.0065 0.0034Table II.Emissivity equivalent to the heat loss through the gas.4. MEASUREMENT PROCEDUREFirst, the two samples are characterized geometrically (diameter of the radiating surface,thickness, positions of the two radial holes).The samples are fasten on the heating system with thermal grease applied between thesamples and the meter plate to provide a good thermal contact, thermal grease is also applied10

etween the sample rings and the guard ring. The thermal grease is used to reducetemperature unbalance between the two sides and between the samples and the rings and toimprove the homogeneity of temperature.The heating system (with the samples and the rings) is suspended at middle height of thevacuum chamber. The air is pumped out until the pressure is below 5 × 10 -3 Pa. The dewar isfilled with liquid nitrogen until the level exceeds of 5 cm the flange of the vacuum chamber.The temperatures of the heating system (meter plate and guard ring) are stabilised at therequired level, the time to get a good stability is about four hours.The temperatures of the two samples and of the two sample rings are measured to control thatthe two samples and the two rings are approximately at the same temperature.The temperatures in the two samples and in the two rings are measured as well as theelectrical power supplied to the meter plate. Those measurements are repeated at least 30times and the mean emissivity is calculated using the model.5. ASSESMENT OF UNCERTAINTIESTable III gives the list of causes of uncertainty that are considered.The numerical values were evaluated for the particular case of a black paint(thickness = 50 µm) applied on copper substrates, the samples were at 20 °C and themeasured total hemispherical emissivity was 0.921.All the uncertainties given in the table are expanded uncertainties with a coverage factork = 2.11

Parameter or modelValue & ExpandedUncertainty (k = 2)Induced expandeduncertainty on themeasured emissivitySurface of the samples 0.00608 ± 4 10 -6 m 2 6.1 x 10 -4Surface of the chamber 1.36 ± 0.1 m 2 3.3 x 10 -4Surface of the samples rings 0.0240 ± 0.0008 m 2 4 x 10 -5Mean total hemispherical emissivity of the 0.92 ± 0.05 1.8 x 10 -3chamber wallsMean total hemispherical emissivity of the 0.8 ± 0.1 1.3 x 10 -4ringsElectrical power 2.31950 ± 7 10 -5 W 2.8 x 10 -5Mean surface temperature of the samples 293.5 ± 0.2 K 2.5 x 10 -3Mean temperature of the chamber walls 78 ± 2 K 5 x 10 -4Mean surface temperature of the rings 293.0 ± 0.2 K 4 x 10 -6Edge heat loss by radiation 0.0076 ± 0.002 W 8 x 10 -4Edge heat loss by conduction between the 0.006 ± 0.01 W 4 x 10 -3samples and the ringsEdge heat loss by conduction between the 0 ± 0.006 W 2.4 x 10 -3meter plate and the guard ringHeat loss by air 0.00073 ± 0.0005 W 2 x 10 -4Model used for emissivity calculation ± 0.001 1 x 10 -3Random variations of measured emissivities ± 0.002 2 x 10 -3Measured Emissivity 0.921 0.0062Table III.Budget of uncertainty for a black paint at 20 °C.6. VALIDATION OF MEASUREMENTSThe measurement technique was validated by comparison with a radiative technique ofmeasurement used at PTB (Physikalisch Technische Bundesanstalt) in Germany. Themeasurement technique of PTB is described in [9]. PTB measured the total directionalemissivity, for many directions between 0° and 75° (angle to the normal), by comparison to a12

lack-body. A total radiometer was used for the comparison. A model of angular variationwas then applied and the hemispherical total emissivity was calculated by integration over thehalf-space.The material selected for the comparison was AISI 304 L stainless-steel. The samples weresandblasted and oxidised by heating in air at 360 °C. The results are givenin Table IV. For LNE, the results are the mean emissivities of the two samples. For PTB, theemissivity given for 40°C is the one measured on sample no.1. For 150°C and 200°C, thevalues are the means of the emissivities measured independently on the two samples. For150°C and 200°C, the differences between the emissivities of the two samples, measured byPTB, are lower than 0.006.The results of the two laborarories are in agreement within the combined uncertainties. Theuncertainties of LNE are much lower than those of PTB, probably because the method ofmeasurement is more direct and requires fewer parameters to be measured (directionalemissivity for PTB). For the temperature 40 °C, the uncertainty of PTB is large because theradiative emission of the sample is low.TempératureTotal hemispherical Emissivity (oxidised AISI 304L stainless steel)LNE PTB PTB - LNE40 °C 0.399 ± 0.0060 0.420 ± 0.04 0.021150 °C 0.427 ± 0.0068 0.433 ± 0.02 0.006200 °C 0.441 ± 0.0075 0.438 ± 0.02 -0.003Table IV.Comparison of the results of PTB and LNE7. CONCLUSIONLNE has developed an apparatus for measuring total hemispherical emissivity of solid opaquematerials. The emissivity can be measured in the temperature range –20 to 200 °C, onmaterials with a thermal conductivity higher than 0.2 W m -1 K -1 . The sources of errors and thesources of uncertainties have been analysed in detail. The sources of errors that have to beconsidered are the parasitic heat fluxes at the edge of the samples.The main sources of uncertainties are :- the uncertainty on the heat flux between the samples and the rings, due to the uncertaintyon the difference of temperature between the samples and the rings,- the uncertainty on the surface temperatures of the samples which depends on theconductivity of the material and of the level of temperature,- the uncertainty on the heat flux between the meter plate and the guard ring.For materials with a thermal conductivity higher than 0.5 W m -1 K -1 , the uncertainty on thetotal hemispherical emissivity remains lower than ± 0.03. This level of uncertainty is verysatisfactory for the majority of the applications which need the knowledge of totalhemispherical emissivity.13

REFERENCES1. M.C. Certiat, O. Mace, Caractérisation expérimentale de l'émissivité : Besoins pourAérospatiale, Méthodes développées, Société Française des Thermiciens, SectionRayonnement, Journée d'étude du 17 Avril 1991 sur Pyrométrie Optique, Mesures desémissivités.2. K. Fukuzawa, A. Ohnishi, Y. Nagasaka, Total Hemispherical Emittance of PolyimideFilms for Space Use in the Temperature Range from 173 to 700 K, Int. Jour. ofThermophysics, Vol. 23, No. 1, January 2002, pages 319-331.3. D. Naws, B. Pouilloux, Total Hemispherical high temperature Emissivity measurementusing the static calorimetric method test specimen feasibility study, High Temp. Chem.Proccesses, 3, February 1994, pages 99-108.4. Thermal insulation -- Determination of steady-state thermal resistance and relatedproperties -- Guarded hot plate apparatus, ISO 8302, 1991, International Organization forStandardization, Geneva, Switzerland5. R. R. Zarr, W. Healy, J. J. Filliben, D R. Flynn, Design concepts for a new guarded hotplate apparatus for use over an extended temperature range, R. R. Zarr, W. Healy, J. J.Filliben, D R. Flynn, Reprinted from STP 1426, ASTM International Standards,Insulation Materials, Testing and Applications, V4, 2002 – ISBN 0-8031-2898-3.6. J. Lorengel and R. Todtenhaup, in Wärmeleitfähigkeit, Gesamtemissionsgrade undspektrale Emissionsgrade der Beschichtung Nextel-Velvet Coating 811-21, PTB-Mitteilungen 106 4/96.7. Y.S. Touloukian , D.P. DeWitt , Thermal Radiative Properties , Metallic Elements andAlloys. Thermophysical Properties of Matter, Volume 7, pages 40a-42a, IFI/Plenum. NewYork–Washington. 1970.8. G. ROMMEL, Gaz à très basse pression – Généralités , Ref B4020, Techniques del’Ingénieur, Paris, 1984.9. J. Lohrengel, Determination of the surface temperature of poor heat conductingmaterials by radiation measurements for -60 °C to +250 °C in vacuum, Wärme- undStoffübertragung, 21 (1987), p. 1-5.14