an approach to thermocouple measurements that reduces uncertainties...

An Approach to Thermocouple Measurements That ReducesUncertainties in High-Temperature EnvironmentsSiddharth Krishnan,†,⊥ Benjamin M. Kumfer,‡ Wendong Wu,‡ Jichuan Li,§ Arye Nehorai,§

and Richard L. Axelbaum*,‡

†Department of Mechanical Engineering and Materials Science, ‡Department of Energy, Environmental and Chemical Engineering,and §Department of Electrical and Systems Engineering, Washington University in St. Louis, One Brookings Drive, St. Louis,Missouri 63130, United States

ABSTRACT: Obtaining accurate temperature measurements with thermocouples in flame environments is challenging due tothe effects of radiative heat losses, as these losses are difficult to quantify. Efforts to minimize radiative losses by, for example,suction pyrometry often result in a significant sacrifice in spatial resolution. In this work, a new experimental methodology ispresented that both minimizes the temperature correction and allows the remaining correction to be accurately quantified. Theapproach is based on increasing and controlling the convective heat transfer to the thermocouple junction, which is accomplishedby spinning the thermocouple at high speed. The rotation yields a large and known convective velocity over the thermocouple.Heat transfer can then be modeled for the thermocouple, and a functional relationship between temperature and rotational speedcan be found. Fitting this model to the data allows for an accurate temperature correction. To test the feasibility of the rotatingthermocouple technique for temperature measurement in high-temperature gases, experiments were conducted over a range ofrotational speeds in a controlled flame where the temperature was known. The measured thermocouple temperatures as afunction of rotational speed closely match the theoretical temperatures, yielding a straightforward approach to highly accurate gastemperature measurement. The results also demonstrate limited perturbation to the flow field, even at high rotational speeds.Finally, a method of deconvolution is described that significantly enhances the spatial resolution of the technique, approachingthat of a stationary thermocouple.

1. INTRODUCTION

Temperature measurements are ubiquitous in combustionsystems. These measurements are useful in a wide range ofapplications, from laboratory-scale flames to large-scale boilersand furnaces. A variety of methods have been employed formaking gas temperature measurements in flames. Broadlyspeaking, these methods can be classified into optical andprobe-based measurements. Though optical approaches to gastemperature measurements provide some advantages overprobe-based methods, they are often difficult to implement,can be costly and cumbersome, and are often not effective inparticle-laden flames.1 Thus, probe-based measurements remainthe method of choice for many combustion studies.Among probe-based measurements, thermocouples have

gained preeminence because they are inexpensive, robust, andeasy to use. Fine-wire thermocouples have been extensivelyused for flame temperature measurements, and their use hasbeen thoroughly described; unfortunately, these measurementsrequire corrections due to radiative and conductive heatlosses.1−6

For fine-wire thermocouples, conduction losses are negli-gible, and thus it is the radiation correction that presents themost difficult challenge to accurate measurement of gastemperatures. Radiation varies with the fourth power oftemperature, so a sharp increase in radiative losses is observedwith increasing gas temperature. At the temperatures typicallyencountered in flame environments the required correctionresulting from these losses can be hundreds of degrees.7,8 Whilethe common challenge in laboratory flames is to correct for

cooling of the thermocouple due to radiation losses from thethermocouple to the environment, heating of the thermocouplecan be significant in the cooler parts of large scale flames wherethe thermocouple is heated by radiation from hot surroundingssuch as furnace walls or from soot particle radiation.8

Correcting for radiation losses or gains is complicated byuncertainties in variables such as the convective heat transfercoefficient, the bead size, shape, and emissivity, and thetemperature and emissivity of the surroundings. The presenceof particles in the flow creates additional challenges. Manysimple algebraic models have been developed to correct forradiation losses from the bead,7 and some have been validatedusing computational fluid dynamics models.9 Radiation gainsdue to radiation from the environment to the bead are systemdependent, and thus no simple models are available for thiscorrection.One approach to radiation correction that has been

extensively discussed is the use of multiple thermocouples(typically two) that are made of identical materials but ofdifferent diameters. In this way it is possible to extrapolate tozero diameter,10,11 In unsteady flows the accuracy of thistechnique is limited by the different time constants of thethermocouples, owing to their different diameters, providing noclear relationship between bead size and temperature, thoughseveral frequency-based compensation techniques have been

Received: January 13, 2015Revised: March 30, 2015

Article

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© XXXX American Chemical Society A DOI: 10.1021/acs.energyfuels.5b00071Energy Fuels XXXX, XXX, XXX−XXX

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http://dx.doi.org/10.1021/acs.energyfuels.5b00071

suggested.11−14 Additionally, there is a dependence on thegeometry and orientation of the thermocouples, which makes itdifficult to implement the technique in practical combustionsystems.Perhaps the most widespread industrial approach to

addressing the problem of radiation correction is the use ofsuction pyrometers, otherwise known as aspirated thermocou-ples, which are designed to minimize radiation losses.8,9,15,16 Asthe name suggests, suction pyrometers locally extract thecombustion gases into a probe. The flow is accelerated withinthe probe so that when it passes over the thermocouple theconvective heat transfer is high and controlled. This highconvective heat transfer brings the thermocouple closer to thegas temperature.Suction pyrometers, however, have important limitations.

They rely on extremely high aspiration velocities, often on theorder of 150 m/s, to minimize the value of the requiredcorrection. This requires suction flow rates on the order of 300L/min, which results in extremely poor spatial resolution andlarge disturbances to the flow field. This high sampling volumecan also mean that suction pyrometers are impossible toimplement in smaller burners. The probes are also large andcumbersome, and can be expensive. Additionally, in particle-laden flows, clogging is a problem, as the molten ash candeposit on surfaces.1,8,17 Finally, the measurement may beaffected by the orientation of the probe, and the probe has avery large time constant due to the shields,1 making themeasurements slow and cumbersome. For example, even at anextremely high aspiration velocity of 250 m/s and an ambienttemperature of 1600 °C, the probe can take up to 3 min toreach equilibrium temperature, and an estimated 1 min for a100 °C increase in temperature.18

Blevins and Pitts8,17 showed that an aspiration velocity of aslow as 5 m/s is usually a significant improvement over an openthermocouple measurement, but operation at this low velocitywill result in high required corrections. For example, when thetrue gas temperature is 927 °C and the surroundings are atroom temperature, the temperature measured with a 1.5 mmthermocouple will increase sharply from 450 to 730 °C whenthe aspiration velocity is increased to 5 m/s, but will notapproach the true gas temperature until the aspiration velocityis increased to 200 m/s,8,17 illustrating the diminishing value inoperating at higher aspiration velocities.The present study seeks to introduce a new experimental

methodology to minimize radiation and conduction losses andallow for accurate determination of temperature correction, andto do this without the level of sacrifice to spatial and temporalresolution that is inherent in aspiration thermocouple measure-ments. This is achieved by means of a high-speed rotatingthermocouple (RTC), which ensures a high and quantifiableconvective heat transfer, thereby minimizing the effects ofradiation and conduction and ensuring an accurate correction.To the best of the authors’ knowledge, thermocouple rotationor translation have not been previously used to reduce therequired radiation correction or to obtain accurate radiationcorrections. A detailed description of the methodology andexperimental system follows.

2. DESIGN CONSIDERATIONS

Figure 1a shows a thermocouple in a flow of hot gas in anenclosure. A simple steady-state heat balance for thisthermocouple bead, as shown in Figure 1b, is given by

+ + =Q Q Q 0conv cond rad (1)

Convection can either heat or cool the bead, depending onwhether the bead is cooler or hotter than the gas, respectively.The bead can lose heat by conduction through its wires, andgain or lose heat through radiative exchange with itssurroundings. If the temperature of the surroundings, Ts, islower than that of the thermocouple bead, Tb, the net radiationheat transfer will be from the bead to the surroundings. Inpractice, the emissivities of the surroundings and the bead canbe difficult to accurately predict. The emissivity of thesurroundings is system-dependent, and in particle-laden flows,it can be particularly difficult to calculate, as it will depend onthe temperatures and the emissivities of the particlesthroughout the entire flow field. In addition, the emissivity ofthe bead can change due to exposure to the flow, as it canundergo chemical changes or be coated with soot or ash.The convective heat transfer can be expressed simply by

Newton’s law of heating/cooling and is equal to the product ofthe temperature difference between the gas and the bead, theconvective heat transfer coefficient, h, and surface area, Asurf.The conductive heat loss is directly proportional to thetemperature gradient across the wire, given by ΔT, the cross-sectional area of the wire, A, and the thermal conductivity of thethermocouple material, kb.The net radiative heat flux entering or leaving the

thermocouple depends on the temperatures of the thermo-couple and the surroundings, the emissivity of the thermo-couple, εb, and the emissivity of the surroundings, εs. Forillustrative purposes, we will assuming that the absorptivity andemissivity of the thermocouple are equal (Kirckoff’s law) andthat the emissivity of the surroundings is unity. Using theseassumptions and the above simplifications, eq 1 can beexpanded and rewritten as

ε σ− + − + Δ =⎛⎝⎜

⎞⎠⎟h T T T T

k ALA

T( ) ( ) 0g b b b4

w4 b

surf (2)

Rearranging eq 2, we get

ε σ= +

− + ΔT T

T T k A LA Th

( ) ( / )g b

b b4

w4

b surf(3)

Figure 1. Schematic illustration of (a) thermocouple in a stream of hotgas and (b) heat flows to and from a thermocouple bead.

Energy & Fuels Article

DOI: 10.1021/acs.energyfuels.5b00071Energy Fuels XXXX, XXX, XXX−XXX

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The second term on the right side of eq 3 represents acorrection or inaccuracy due to radiative and conductive heatlosses. Increasing the value of the convective heat transfercoefficient, h, minimizes the value of the correction. The valueof h can be calculated from the Nusselt number, which is afunction of the Reynolds number and Prandtl number. Ageneralized form for the Nusselt number is given by

= =Nu C Re Pr hD k/m nD g (4)

The constants C, m, and n vary for different thermocouplegeometries, Reynolds numbers, and gas compositions. Solvingeq 4 for h and plugging into eq 3 yields

ε σ= +

− + ΔT T

T T k A LA TC Re Pr k D

( ) ( / )( / )m ng b

b b4

w4

b surf

g (5)

Equation 5 contains a number of terms that are difficult toaccurately quantify in laboratory- and industrial-scale flames.The uncertainties in the emissivities of both the surroundingsand the bead have already been discussed. The gas properties,such as the Prandtl number and kg, are dependent ontemperature and composition, which are typically unknown.The Reynolds number is dependent on the local gas velocityover the thermocouple bead, Vg, which is also typicallyunknown. Moreover, in a turbulent system, Vg fluctuates,further complicating interpretation since the heat balancebecomes an unsteady problem and the thermal mass of thebead becomes important.While inherent uncertainties in thermocouple measurement

can exist (for example, from installation errors of thethermocouple, signal errors in the transmission wires, analog-to-digital (A/D) conversion, and conversion to temperaturefrom voltage),19 these uncertainties are typically small for flametemperature measurements and can often be ignored.Many of the challenges associated with thermocouple

measurements in flames can be circumvented if thethermocouple is rotated at high speed, as will be explainedbelow. The linear speed of the bead, Vb, is a function of therotational speed, ω, and, if the rotational speed is fast enoughthat the surrounding gas velocity is small compared to Vb, thenVrel, the total relative velocity between the bead and the gas, canbe approximated by

π ω≈Vr2

60rel (6)

where r is the radius of the circular motion of thethermocouple, as shown in Figure 2. Here r is a designparameter and dictates how rotational speed translates intolinear speed. This demonstrates one of the benefits of spinningthe thermocouple: while the gas velocity over a thermocouple istypically unknown, spinning the thermocouple at sufficientlyhigh speeds removes this uncertainly since the gas velocity over

the thermocouple can be determined from the knownrotational speed of the thermocouple.Combining eqs 5 and 6, we obtain

ε σ

π ρ μ ω− =

− + Δ

( )T T

T T k A LA T

C rD Pr k D

( ) ( / )

[(2 /60 ) ] /m ng bb b

4w

4b surf

b g b (7)

Equation 7 provides us with a functional relationship betweenthe rotational speed, the diameter of the thermocouple, Db, andthe correction. The denominator varies as ωm, indicating that asthe rotational speed is increased, the magnitude of thecorrection is decreased. The exponent m is typically around0.5.20 This demonstrates a second important benefit ofspinning the thermocouple: the large relative velocity of thegas over the thermocouple leads to an increase in theconvective heat transfer coefficient, which decreases theradiation and conduction corrections.To gain an appreciation for the magnitude of the effect of

spinning for realistic values of rotational speed and bead size,the following assumptions are made. A flame temperature of1500 °C is used, and r is assumed to be 12 mm. The gasproperties are evaluated at 1500 °C and are assumed fornitrogen since a large fraction of the combustion gas is typicallynitrogen. The kinematic viscosity, ν, is taken to be 27.5 × 10−5

m2/s, the thermal conductivity, k, to be 0.09 W/m-K, and thePrandtl number to be 0.73. The temperature of thesurroundings, Ts, is taken to be 300 K. An emissivity of 0.1,that of uncoated platinum, is assumed for the thermocouplebead, and conduction losses are neglected.In Figure 3, the normalized bead temperature, T*, defined as

the ratio of the thermocouple bead temperature Tb to the true

gas temperature Tg in °C, is plotted as a function of rotationalspeed for various bead diameters. The normalized beadtemperature is obtained from eq 7 using the Churchill−Bernstein correlation20,21 for flow over a cylinder. The smallerthermocouple bead size results in smaller radiative lossesbecause of the reduced surface area. A key observation fromthis figure is that the effect of rotational speed on T* issignificant, and T* approaches unity for sufficiently fine-wirethermocouples and rotational speeds around 20 000 rpm.Based on this information, an experimental apparatus was

constructed to test the feasibility of this concept for measuringgas temperature in hot environments.

3. EXPERIMENTAL SECTIONA schematic of the system is shown in Figure 4. A hollow shaft madeof 347 stainless steel is fitted with a platinum−platinum/rhodium 10%Figure 2. Schematic illustrating the quantities Vrel, ω, and r.

Figure 3. Normalized temperature, which is the ratio of thethermocouple bead temperature, Tb, to the true gas temperature, Tg(both in °C), plotted as a function of rotational speed.



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(Type S) thermocouple. The dimensions of the shaft are 12.7 mmouter diameter, 3.18 mm inner diameter, and 165 mm length. Thediameter of the thermocouple wire is 0.13 mm, and the diameter of thebead in these experiments is 0.20 mm. The wire diameter chosenrepresents an optimum, as it is significantly more robust than finerwire thermocouples while also being thin enough to minimizeconduction losses. Tests were also conducted with a 0.05 mmdiameter thermocouple, and stroboscopic measurements revealed thatthe thermocouple maintained its shape and did not deform while beingspun. Nonetheless, fine wires of this size are not robust. Since theprimary drawback of the larger wire size is the larger corrections due toradiation and conduction, which this work seeks to address, mostexperiments were conducted with the larger wire size of 0.13 mmdiameter.The thermocouple wire is housed inside an alumina ceramic tube.

The wires protrude 14 mm from holes in the ceramic tubing and arebent at nearly right angles to the longitudinal axis of the shaft, therebycreating a radius of 14 mm. This radius represents somewhat of anoptimum. A smaller radius would require a higher rotational speed tocreate the same velocity, while a larger radius represents a largersampling area and reduced spatial resolution.The shape of the thermocouple bead more closely resembled a

cylinder than a sphere, though it was not perfectly cylindrical. As willbe shown, with the RTC it is not necessary to know the exact shape ofthe thermocouple.The shaft is mounted to an AC motor that is equipped with a

variable speed control, and the rotational speed can be varied from 0 to23 000 rpm. The rotational speed is measured using a noncontact lasertachometer. The low-voltage thermocouple signal is transmitted bymeans of a slip ring-brush system (Fabricast Inc., South El Monte,California) that is specifically designed for thermocouple measure-ments. The analog signal is converted into a digital temperaturereading using an MC USB-TC (Measurement Computing, Norton,MA) A/D board. The signal is converted to a temperature using aType S calibration curve and fed to a computer, where it is recorded inreal-time using LabView (National Instruments, Austin, TX) software.An important goal of this feasibility study is to experimentally

determine the functional relationship between Tb and ω. Once this isobtained, the value for Tg that is determined from this functionalrelationship can be validated by comparing it with the value of Tgobtained from a stationary thermocouple. The stationary thermocou-ple is placed under conditions where the radiation correction can beestimated accurately to within 20 °C; thus, this temperature is treatedas a known reference temperature.

To perform such a calculation, a McKenna premixed flat-flameburner was used to generate the experimental flame because it has acontrolled and quantifiable local velocity and a well-characterizedtemperature distribution.22,23 The RTC assembly was mounted overthe 60 mm diameter burner head, which is composed of sinteredstainless steel and is water-cooled. The burner was fed with apropane−air mixture and was shielded with an inert nitrogen shroud.The bead of the thermocouple was positioned 7.5 mm above thevisible flame, and no disturbance to the flame was perceptible underthese conditions. The sampling rate for these experiments wasarbitrarily chosen to be 2 Hz, as the flame was steady and displayednegligible temporal variation in temperature. Three flames wereproduced for the experiments, with equivalence ratios of φ = 1.0, 0.85,and 0.70. The air flow rate was held constant at 2.3 kg/h, while theflow rate for propane was 0.092, 0.073 kg/h or 0.068 kg/h to yield thethree equivalence ratios and a gas flow velocity of ∼1.2 m/s. Catalyticeffects, while often significant, can be neglected here because thethermocouple was in the post-flame region and the premixed systemwas operated with a fuel-lean stoichiometry.

The RTC assembly was mounted such that the plane of rotation forthe thermocouple was parallel to the surface of the flat-flame burner.In other words, the bead was a fixed height above the burner headduring its rotation. However, the McKenna burner is not truly one-dimensional, as temperature gradients exist along the surface of theburner.24 To address this and ensure that the gas temperature alongthe path of the spinning thermocouple was nearly constant, a portionof the burner that displayed minimal temperature variations wasidentified and used. This is important because when the thermocouplerotates it traces out a circumference of 88 mm. For the region of theburner that was used, a temperature variation of 35 ± 5 °C wasobserved for the three flames that were used in this study. To obtainthe average thermocouple temperature over this circumference,stationary temperature measurements were taken at 44 points aroundthe circumference, with each measurement 2 mm apart, and theaverage of these measurements was computed. A radiation correctionwas then performed on this average temperature to yield the averagegas temperature Tg,ref along the path of the thermocouple bead.

Additionally, a control thermocouple was constructed of Pt 30%Rh−Pt 6% Rh (Type B) alloy, with 0.20 mm bead diameter. Thisthermocouple was placed in the flame at the same height as the RTC±1 mm, but at a distance of 5 mm from the RTC at its closest locationduring rotation. This second thermocouple was used to evaluate theeffect of flame perturbation caused by the high-speed rotation, and thedata were recorded simultaneously with the RTC as part of the sameexperiment, also at a sampling rate of 2 Hz.

The stainless steel supporting rod and motor, shown in Figure 4,were not cooled in this experiment because the heat from thecombustion products could be easily shielded from the rod and othercomponents, so that the temperatures were never too high. In largerscale system, for example in a furnace, these parts would need to becooled to ensure that the temperatures of these components are nevertoo high. In particular the stainless rod, which must protrude into theflame, would need to be shielded, e.g., with a water jacket, to keep itfrom warping.

The slip-ring bearings exhibited frictional heating. This heating ledto predictable errors in the signal, which were on the order of 7 °C at10 000 rpm, and virtually nonexistent below 5000 rpm. The error wascorrected for by using a calibration.

4. RESULTS

Photographs of the RTC were taken at various rotationalspeeds and are shown in Figure 5. The photograph in Figure 5awas taken with an aperture setting larger than that forsubsequent photographs to clearly illustrate the flat flame andthe relative position of the RTC. The photographs in Figure5b−d were taken with a smaller aperture setting to avoidsaturation and clearly show differences in the brightness of the

Figure 4. Schematic of experimental setup.



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RTC with rotational speed. The increased brightness of theRTC at 7000 rpm over that at 3000 rpm is clearly visible.To accurately quantify the dependence between the bead

temperature and the rotational speed, separate flames wereproduced, each with a different equivalence ratio. Thethermocouple was rotated at a range of rotational speedsbetween 0 and 10 000 rpm and allowed to come to steady stateat each speed. The signal was averaged over 10 s to reducenoise, and these values are shown in Figure 6 along with acurve-fit of the data. The fluctuation in temperature at eachspeed was minimal, on the order of 1 °C. The fluctuation intemperature, along with other uncertainties, such as errors inthe thermocouple calibration, are included in the error bars.An important goal of this work is to validate the RTC

technique, and to do this the gas temperature was obtained fora stationary thermocouple. For this particular burner, the gasvelocity can be accurately predicted, because the burner massflow rate is known and the flow rate exiting the burner is nearlyuniform. Thus, a rather accurate temperature correction can bemade for the stationary thermocouple, and this radiation-corrected temperature is a reference gas temperature, Tg, ref, thatcan be compare to the curve-fitted gas temperature for theRTC, Tg, RTC. In Figure 6, Tg, ref is shown as the horizontaldashed line.To obtain the gas temperatures from the curves, no

assumptions were needed as to the thermocouple shape andgeometry. The gas properties are assumed to be those of air at1350, 1300, and 1240 °C, respectively; r/L, the inverse aspectratio, was measured to be ∼0.005; and the emissivity of thethermocouple bead is assumed to be 0.1, that of uncoatedplatinum. The data were fitted to the general form for theNusselt number given in eq 4, and yielded the following valuesfor the fitting constants: C = 0.6, m = n = 0.5, and Pr = 0.69,

which are consistent with values reported in the literature. Thequality of the fit is illustrated by r2 values of 0.99, 0.99, and 0.95,respectively, for the three data sets. It is important to note thatthe values for C, m, and n obtained represent actualexperimentally obtained constants and are thus more accuratethan just pulling these values from the literature for idealizedsystems (e.g., by assuming spherical or cylindrical bead shapes).For the RTCs the relative velocity of the gas over the

thermocouple bead was obtained from rotational speed,neglecting the actual gas velocity since it was small compared

Figure 5. Photograph of the RTC and the McKenna flat-flame burnertaken at (a) 0 rpm and with a large camera aperture setting, and at (b)0, (c) 3000, and (d) 7000 rpm with a smaller aperture setting. Thecamera settings for aperture and shutter speed were constant in panelsb−d.

Figure 6. Relationship between temperature and rotating speed forRTC. Experimental temperatures measured by RTC plotted againstrotational speed for (a) φ = 1.0, (b) φ = 0.85, and (c) φ = 0.70. Theradiation-corrected gas temperature is presented with the horizontaldotted line, and the curve fit predicted by the theory is included foreach flame.



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to the velocity of the bead, except at lower rotational speeds(<3000 rpm). Conduction losses are negligible here because ofthe high aspect ratio of the thermocouple wire. The gastemperatures obtained from curve-fitting the RTC data, Tg,RTC,at the three different equivalence ratios (1, 0.85, 0.7), are within7, 17, and 1 °C, respectively, of the values obtained from theradiation-corrected stationary thermocouple data Tg,ref. Theseresults are summarized in Table 1.

5. DISCUSSIONValidity of the Technique. The result shown in Figure 5

demonstrate the dynamics of the RTC: increasing rotational

speed yields an increase in bead temperature due to theincrease in convective heat transfer and thus reduction inradiation correction. Increasing convection to reduce theradiation correction is analogous to what is done in a suctionpyrometer. However, if the technique simply relied on highconvection, then the accuracy would be severely limited, aseven at rotational speeds as high as 10 000 rpm the correctionsare still on the order of 150 °C. As can be seen from the formof the curves in Figure 4, the benefit of increasing speeddiminishes at high speeds. This is also true for suctionpyrometers as well, but suction pyrometers also suffer fromlosses in spatial resolution and greater disturbances at highaspiration velocity. In the RTC, the thermocouple wire is thin

(0.13 mm), and at rotational speeds of 10 000 rpm, theReynolds number is around 30, resulting in a relatively thinboundary layer and a small flow perturbation.More saliently, the high-speed rotation controls and defines

the local velocity, and therefore the local convective heattransfer coefficient can be accurately predicted. The minimalnumber of assumptions that are required to yield good curvefits suggests the ability to accurately predict gas temperaturewith low uncertainty. The value of gas temperature predicted bythe RTC is within 17 °C of Tg,ref. Additionally, the values of thefitting parameters correspond very well to values reported inthe literature, and this serves as further validation of the fittingtechnique. It is highly likely that the curve-fitted value is, in fact,more accurate than Tg,ref, since Tg,ref was obtained from aradiation correction that required an assumption about beadshape and the functional form of the Nusselt numbercorrelation. Moreover, this accuracy is virtually impossible toattain with a suction pyrometer because the flow rates do notapproach infinity, the gas sample volume is large, and themeasurement times are long.

Spatial Resolution. The improvement in spatial resolutionof the RTC over the suction pyrometer represents a significantadvantage of the technique. Furthermore, to increase theaccuracy of Tg,RTC the rotational speed can be increased, butwhen this is done the circumference over which the RTCaverages the temperature (i.e., the spatial resolution) does notchange. This means that there is no trade-off between accuracyand spatial resolution in the RTC. This is not the case with thesuction pyrometer: the accuracy of the measurement increaseswith the amount of gas aspirated into the suction pyrometer,but the spatial resolution is worse. Suction pyrometer velocitiescan be as high as 200 m/s, leading to poor spatial resolution.

Averaging over the Circumference Traced Out by theRotating Thermocouple Bead. The RTC measures anaverage temperature in space and time. Figure 7a shows thecircle traced out by an RTC with a rotational radius r, rotatingat a speed ω in an in arbitrary stationary temperature field. Anillustration of the instantaneous temperature of the bead isshown in Figure 7b. The temperature field is shown to bevarying in space along the path of the thermocouple. If theRTC were allowed to reach steady state at each angle θ alongthe circumference, then it would measure the temperaturedistribution Tb,θ (ω = 0). This is represented by the solid curvein Figure 7b. When ω is greater than zero, the RTCtemperature lags behind the stationary temperature due tothe thermal mass of the thermocouple bead and the resultingtime constant of the RTC. This flattens the Tb curve, the extent

Table 1. Radiation-Corrected Gas Temperatures and GasTemperatures Predicted with RTC

Φ Tg, ref (°C)a Tg,RTC (°C)b

1.0 1347 13400.85 1301 12840.70 1234 1235

aObtained from radiation correction to stationary thermocouplemeasurement. bObtained by curve-fitting RTC data.

Figure 7. Illustration of the influence of rotation on the measuredtemperature. (a) RTC rotating with a radius r and a rotational speed ωin a temperature field. (b) The instantaneous temperature measuredby the RTC in the temperature field at different rotational speeds.

Table 2. Calculated Relative Magnitude of RotatingThermocouple Time Constant and Rotational Speed

at 5000 rpm at 10 000 rpm

beaddiameter(mm)

timeconstant

(s)

no. of circles sweptin one timeconstant

timeconstant

(s)

no. of circles sweptin one timeconstant

0.30 0.46 38 0.36 600.20 0.24 20 0.19 320.13 0.11 9 0.09 15

Figure 8. Schematic of deconvolution operation. The coordinates x1and y1 represent arbitrary points in a 2-D plane with a temperaturedistribution f(x1,y1). The rotation of the thermocouple results in acircularly swept region, represented by the circles, and a measuredtemperature g(x1,y1).



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to which is dictated by the time constant, τb, at a given ω. As ωis increased, Tb,θ(ω) further flattens out, as shown in Figure 7bby curves Tb,θ(ω1) and Tb,θ(ω2).Table 2 shows the relative magnitude of the RTC time

constant, τb, and the time taken to traverse the circle at tworotational speeds of interest, for a range of bead diameters. It isapparent that at rotational speeds of 5000 and 10 000 rpm, τb ismuch longer than the time it takes to traverse the circum-ference one time, and thus, at sufficiently high rotationalspeeds, the measured bead temperature is the averagetemperature across the circumference.If the temperature field that the RTC is spinning in

experiences a change on a time scale that is significantly longerthan τb, then it can completely capture this change, as a normalnonrotational thermocouple would. Similarly, if the temper-ature field changes on a time scale that is significantly shorterthan τb, then the RTC would not be able to capture thesechanges. If the change were on the order of the time-constantof the thermocouple, then the rotation would average themeasurement in both space and time.Deconvolution To Improve Spatial Resolution. We

have shown that the RTC measures an averaged temperatureTb,m for practical rotational speeds and RTC time constants.Thus, the spatial resolution of a single RTC measurement isdictated by the region that is swept out by the RTC. However,when the RTC is traversed across a given temperature field theactual temperature field is contained within the convolvedtemperature field. Thus, deconvolution of this field can yield anincrease in spatial accuracy. Below we construct a methodologyby which the RTC measurements in a temperature field can bedeconvolved to yield spatial resolution approaching that of thediameter of the thermocouple bead.We consider the RTC as a system, the original temperature

field as the input of the system, and the measured temperaturefield as the output of the system. The RTC system is describedby its impulse function, which is defined as the output of thesystem with the input being a Dirac delta function at the originof the space. We denote the impulse function of the RTC

system as h, the original temperature field as f, and themeasured temperature field as g. These are illustrated in Figure8. Then, according to the theory from ref 25, we have

= ∗g f h (9)

where the asterisk denotes the operation of convolution. Inorder to determine the original temperature distribution f fromthe measured distribution g, we need to solve an inverseproblem of eq 9, or in other words a deconvolution problem.Assume the radius of an RTC to be r. Suppose that the

investigated temperature field is on a two-dimensional plane.For any point (x1,y1) on the two-dimensional plane, we denotethe original temperature as f(x1,y1) and the measuredtemperature of the RTC as g(x1,y1). Thus, g(x1,y1) is theaverage of f(x,y), where (x,y) is r away from (x1,y1), or in otherwords the average temperature on the circle centered at (x1,y1)with radius r. As the RTC sweeps across the two-dimensionalplane, as represented by the dotted circles in Figure 8, werecord the circle average as our measured temperature at thecenter of the circle.Since the temperature field is continuous, the average along a

circle is in fact an integral in mathematics, which makes theinverse problem intractable to solve. For convenience, weapproximate the temperature field as a discrete grid with eachblock in the grid taking as its value the average temperatureover the area it covers. (Note that the size of a blockdetermines the resolution of the discretization.) Then, we canreplace the original coordinates of a point (x,y) with a two-dimensional integer block index (m,n), which makes thetemperature distribution appear in the format of a matrix. Also,the measured temperature at a block (m1,n1) is approximated asthe average temperature over blocks that are intersected by thecircle centered at the center of the block (m1,n1) with radius r.Since the temperature field is discretized, the number ofintersected blocks is finite, and thus the average is simply anarithmetic average, instead of an integral. Let N be the numberof intersected blocks, then the impulse function of the RTCsystem can be approximated as a matrix where those intersected

Figure 9. Results of deconvolution simulation: (a) original temperature distribution, (b) measured temperature distribution from the RTCmeasurement, (c) deconvolved temperature distribution, and (d) distribution of error, in °C, after deconvolution operation.



G


Table

3.Summaryof

AdvantagesandDisadvantages

ofVarious

Therm

ocou

pleMeasurementsof

Flam

eTem

perature

fine-wire

thermocouple

suctionpyrometer

high-speed

RTC

Accuracy

high

moderate

very

high

Minimizes

radiationlosses,thoughthey

may

still

bepresent.

Inaccuracies

ofhundreds

of°C

canpersist,even

with

high-speed

aspiratio

n.Can

fitdata

totheory

togettrue

gastemperature.

SpatialResolution

very

high

poor

high

Limitof

resolutio

nissurfacearea

offine-wire

thermocouple,on

theorderof

10−9m

2 .Can

beon

theorderof1m

2 ;significant

trade-off

betweenincreasedaccuracy

andspatial

resolutio

n.

Can

deconvolve

measurementsto

achievespatialresolutio

napproachingthat

ofstationary

thermocouple.Notrade-off

betweenaccuracy

andspatialresolutio

n.

Tem

poralResolution

extrem

elyhigh

very

poor

high

Owingto

smallmassof

thermocouple;

timeconstant

ontheorderof

50−100ms.

Due

topresence

ofshields;tim

econstant

onthe

orderof

minutes.

Timeconstant

ishigher

than

that

offine-wire

thermocouple,butRTCalso

averages

over

spaceandtim

e,so

temporalresolutio

nisnotas

high

asthat

offine-wire

thermocouple.

MechanicalIntegrity

very

poor

very

high

moderateto

high

Extrem

elyfragile.

Due

topresence

ofshields.

Therm

ocouplewire

diam

eter

islarger

than

thatof

afine-wire

thermocoupleandcan

beshielded,b

utnotcompletelyenclosed

likesuctionpyrometer.

TimeToTakeMeasurement

very

low

very

high

very

low

Due

topresence

ofshield.

Maintenance

very

high

very

high

anticipated

tobe

low

Fragility

causes

frequent

breakage,p

articularlyin

particle-ladenflow

s.Due

toclogging.



H


blocks or elements take the value of 1/N and the others takethe value of 0.After discretization, f, g, and h all become two-dimensional

matrices. Considering the structural similarity between a matrixand an image, we apply to our problem a deconvolutionalgorithm developed for image recovery. Deconvolution isfrequently used in image recovery, and some populardeconvolution algorithms are introduced in ref 26. We solveour problem using the constrained least-squares (regularized)filtering algorithm, which has a corresponding built-in functionnamed “deconvreg” in MATLAB (The Mathworks, NatickMA).Figure 9 shows the results of the deconvolution simulation.

In Figure 9a, a temperature distribution is assumed between 20and 1000 °C over a two-dimensional plane that is 100 mm ×100 mm. The plane is then discretized with each grid squaremeasuring 1 mm × 1 mm. An RTC with rotational radius 10mm, chosen for computational convenience, is then sweptacross the plane in both the x- and y-directions, with each newRTC measurement centered at the next grid point. This“measured” distribution, g(x,y) is shown in Figure 9b. Thedeconvolution operation is then applied to the measureddistribution in Figure 9b and yields a deconvolved temperaturedistribution, shown in Figure 9c and aimed to approximate theoriginal temperature distribution in Figure 9a.The deconvolved distribution is in excellent agreement with

the original distribution. The RMS error of the deconvolveddistribution is 0.37 °C, while the RMS error of the measureddistribution is 24 °C. The distribution of this error for thedeconvolved distribution is shown in Figure 9d.Required Modifications for Use in Industrial Systems.

This work represents a proof-of-concept for the RTCtechnique; however, in order to be viable for use in forindustrial-scale, particle-laden flows, a number of designmodifications are required. In order to obtain temperaturesinside of a combustion chamber the probe would need to becooled with, for example, a cooling jacket to protect the probefrom the high-temperature environment. A cooled extension tosupport and move the probe would be required as well. Finally,in order to protect the RTC from excessive particles, a particleshield would be required. The particles, having a high Stokesnumber, would strike the shield, leaving a particle free region inthe wake of the shield, while the gases would flow around theshield. The shield would need to be spaced sufficiently far fromthe thermocouple to ensure that the gas temperature is notaffected by the presence of the shield. These discussions aresummarized in Table 3.

6. CONCLUSIONSIn this work, the challenges associated with making accuratetemperature measurements with thermocouples in radiatingflame environments are summarized, as are the limitations oftechniques currently in use. A rotating thermocouple method ispresented that seeks to alleviate many of the inaccuracies thatlimit thermocouple temperature measurements. An experimen-tal system was constructed to test the ability of a RTC to makeaccurate flame temperature measurements. Data collectedbetween 0 and 10 000 rpm were fitted to a general functionalform derived for the RTC, and the results demonstrate that theRTC can be used to obtain highly accurate gas temperatures.Gas temperatures measured with the RTC data were within±17 °C of the temperatures measured by a radiation-correctedfine-wire thermocouple, well within the margin of error for such

a measurement. Radiation-corrected fine-wire thermocouplemeasurements can be highly accurate, but they are subject touncertainties associated with the local flow characteristics andthe thermocouple shape. The RTC technique does not requirethis information, and obtains the unknown heat transferparameters by fitting the data to the well-known functionform for the thermocouple temperature corrections, thusyielding high-temperature accuracy. The spatial resolution ofthe measurement, while significantly superior to that of asuction pyrometer, is not as good as that of a single fine-wirethermocouple, as there is spatial averaging associated withrotation at high speeds, dictated by the radius of rotation of thethermocouple. A deconvolution technique is presented in thiswork to yield significant improvements in spatial resolution,approaching, but inferior to, the resolution of a fine-wirethermocouple. The device can be used in large flames, but itcan also be used in smaller flames, as low as 5 kW, which aretoo small for a suction pyrometer.

■ AUTHOR INFORMATION

Corresponding Author*Tel: 01-314-935-7560. Fax: 01-314-935-7211. E-mail:[email protected].

Present Address⊥S.K.: Department of Materials Science and Engineering,University of Illinois at Urbana−Champaign Urbana, IL 61801,USA

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The authors acknowledge Yosef Santer, George Pires, and JohnKreitler for their support in the design and construction of theexperimental system.

■ NOMENCLATURE

A = area (m2)D = diameter (m)h = convective heat transfer coefficient (W/m2-K)RTC = rotating thermocoupleL = length (m)Q = heat flux (W)r = radius (m)T = temperature (°C)V = velocity (m/s)ω = rotational speed (revolutions per min, rpm)σ = Stefan−Boltzmann constant (5.67051 × 10−8 W/m2-K4)ε = emissivityk = thermal conductivity (W/m-K)μ = dynamic viscosity (kg/m-s)ρ = density (kg/m3)t = time (s)τ = time constant (s)Subscriptsb = bead (thermocouple bead)g = gass = surfacew = wallDimensionless NumbersBi = Biot numberNu = Nusselt numberPr = Prandtl numberRe = Reynolds number



I

mailto:[email protected]


■ REFERENCES(1) Heitor, M. V.; Moreira, A. L. N. Thermocouples and sampleprobes for combustion studies. Energy Combust. Sci. 1993, 19 (3),259−278.(2) Sato, A.; Hashiba, K.; Hasatani, M.; Sugaiyama, S.; Kimura, J. Acorrectional calculation method for thermocouple measurements oftemperatures in flames. Combust. Flame 1975, 24, 35−41.(3) Viskanta, R.; Menguc, M. P. Radiation heat transfer incombustion systems. Prog. Energy Combust. Sci. 1987, 13 (2), 97−160.(4) Sbaibi, A.; Paranthoen, P.; Lecordier, J. C. Frequency response offine wires under simultaneous radiative-convective heat transfer. J.Phys. E: Sci. Instrum. 1989, 22 (1), 14.(5) Lecordier, J. C.; Dupont, A.; Gajan, P.; Paranthoen, P. Correctionof temperature fluctuation measurements using cold wires. J. Phys. E:Sci. Instrum. 1984, 17 (4), 307.(6) Lockwood, F. C.; Moneib, H. A. Fluctuating temperaturemeasurements in turbulent jet diffusion flame. Combust. Flame 1982,47, 291−314.(7) Bradley, D.; Matthews, K. J. Measurement of High GasTemperatures with Fine Wire Thermocouples. J. Mech. Eng. Sci.1968, 10 (4), 299−305.(8) Blevins, L. G.; Pitts, W. M. Modeling of bare and aspiratedthermocouples in compartment fires. Fire Safety J. 1999, 33 (4), 239−259.(9) Kim, S.C On the Temperature Measurement Bias and TimeResponse of an Aspirated Thermocouple in Fire Environment. J. FireSci. 2008, 26 (6), 509−529.(10) Brohez, S.; Delvosalle, C.; Marlair, G. A two-thermocouplesprobe for radiation corrections of measured temperatures incompartment fires. Fire Safety J. 2004, 39 (5), 399−411.(11) Tagawa, M.; Ohta, Y. Two-thermocouple probe for fluctuatingtemperature measurement in combustionRational estimation ofmean and fluctuating time constants. Combust. Flame 1997, 109 (4),549−560.(12) Katuski, M.; Mizutani, Y.; Matsumoto, Y. An improvedthermocouple technique for measurement of fluctuating temperaturesin flames. Combust. Flame 1987, 67 (1), 27−36.(13) Hung, P.C; Irwin, G.; Kee, R.; McLoone, S. Difference equationapproach to two-thermocouple sensor characterization in constantvelocity flow environments. Rev. Sci. Instrum. 2005, 76 (2),No. 024902.(14) Bradley, D.; Lau, A. K. C.; Missaghi, M. Response ofCompensated Thermocouples to Fluctuating Temperatures: Com-puter Simulation, Experimental Results and Mathematical Modelling.Combust. Sci. Technol. 1989, 64 (1−3), 119−134.(15) Newman, J. S.; Croce, P. Simple Aspirated Thermocouple forUse in Fires. J. Fire Flammability 1979, 10 (4), 326−336.(16) Z’Graggen, A.; Steinfeld, A.; Friess, H. Gas temperaturemeasurement in thermal radiating environments using a suctionthermocouple apparatus. Meas. Sci. Technol. 2007, 18 (11), No. 3329.(17) Pitts, W. M.; BraunE., Peacock, R. D.; Mitler, R. D.; Johnsson,H. E.; Reneke, E. L.; Blevins, L.G. Temperature Uncertainties for Bare-Bead and Aspirated Thermocouple Measurements in Fire Environ-ments. Proceedings, ASTM STP 1427, December 3, 2001, Dallas, TX;American Society for Testing and Materials: West Conshohocken, PA,2002.(18) IFRF, Doc. No. c76/y/1/17b; International Flame ResearchFoundation: Livorno, Italy, 2009.(19) Nakos, J. T. Uncertainty Analysis of Thermocouple Measure-ments Used in Normal and Abnormal Thermal EnvironmentExperiments Sandia’s Radiant Heat Facility and Lurance CanyonBurn Site, SAND2004-1023; Sandia National Laboratories: Albu-rquerque, NM, 2004.(20) Incropera, F. P.; DeWitt, D. P.; Bergman, T.; Lavine, A.Fundamentals of Heat and Mass Transfer, 6th ed.; John Wiley and Sons:New York, 2007:(21) Churchill, S. W.; Bernstein, M. A Correlating Equation forForced Convection From Gases and Liquids to a Circular Cylinder inCrossflow. J. Heat Transfer 1977, 99 (2), 300−306.

(22) Sutton, G.; Levick, A.; Edwards, G.; Greenhalgh, D. Acombustion temperature and species standard for the calibration oflaser diagnostic techniques. Combust. Flame 2006, 147 (1−2), 39−48.(23) Gregor, M. A.; Dreizler, A. A quasi-adiabatic laminar flat flameburner for high temperature calibration. Measurement Sci. Technol.2009, 20 (6), No. 065402.(24) Migliorini, F.; DeIuliis, S.; Cignoli, F.; Zizak, G. How “flat” is therich premixed flame produced by your McKenna burner? Combust.Flame 2008, 153 (3), 384−393.(25) Oppenheim, A. V.; Willsky, A. S. Signals and Systems, 2nd ed.;Prentice Hall: Upper Saddle River, NJ, 2013.(26) Gonzalez, R. C.; Woods, R. E.; Eddins, S. L. Digital ImageProcessing Using MATLAB; Prentice Hall: Upper Saddle River, NJ,2004.



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an approach to thermocouple measurements that reduces uncertainties...

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