Method for spectroradiometric temperature measurementsin two phase flows. 2: Experimental verification

Phillip H. Paul and Sidney A. Self

A new method for emission-absorption pyrometric measurements has been developed to account for the

effects of scattering particles suspended in an absorbing gas. In this paper, the principles of this newtechnique are outlined and the results of a series of verification experiments are presented.

1. Introduction

Emission-absorption pyrometry can be used tomeasure the temperature of a uniform plane layercomposed of an absorbing gas at a temperature TG withsuspended absorbing-scattering particles at a tem-perature Tp.1 The distal boundary is illuminated withradiation from a broadband source (a tungsten lamp,say) with a brightness measurement TL which is knownby reference to a suitable standard. With appropriateoptical elements the lamp is imaged into the layer andthen through a suitable spectral selection element tosome detector. With the detector voltage proportion-al to the incident radiance, three signals are required toperform the measurement: the emission signal SGwith the reference lamp blocked, the reference signalSL in the absence of the gas, and the signal SG+L pro-duced with the lamp transilluminating the gas. Thespectral radiance at the detector with the lamp transil-luminating the gas is given by the integrated equationof transfer2

Ix(d) = I(B)(TL) exp(-r\) + I(B)(TL)(wX,r",U), (1)

where I(B) is the Planck blackbody radiance. Thequantity (o.x, Ux,rx) is the spectral emittance of thelayer in terms of the total optical depth

rX (aXG + aXP + a\)d, (2)

the total albedo is

The authors are with Stanford University Department of Me-chanical Engineering, High Temperature Gasdynamics Laboratory,Stanford, California 94305.

Received 19 August 1987.0003-6935/89/112150-06$02.00/0.© 1989 Optical Society of America.

WX =-aXG + aXP + (TX

Ux a Fxp C 1 1 ) \- expi- I;-y li iX LXV UP JG

(3)

(4)

Here aXG is the gas absorption coefficient, aexp and oare the particle suspension's absorption and scatteringcoefficients, respectively, C2 is the second radiationconstant, and X the measurement wavelength.

From the three measured signals, Eq. (1) can be usedto obtain the optical depth via

SG+L - SG

SL

and a simple algorithm for the gas temperature

TG =TL

(5)

(6)TL FSG 11- lnI- Iwx

Equation (6) is the generalized emission-absorptionpyrometric algorithm. When the medium can betreated as purely absorbing, (x 0 0), then the emit-tance of the plane layer is given by

= 1- exp(-rP) = SG + SL - SG+LSL

In part 11 of this paper a relation for the emittance ofan emitting, absorbing, and scattering plane layer wasderived in the form

¢t = [1- (1- U\)wA[(1 + w\)A(r.) - E A;(rO)] (8)1=0

where A and A' are known functions. Invoking a set ofassumptions described in part 1,1 measurements madeat two or three wavelengths simultaneously can beused to obtain the values of r, wA, and UA and thus (P.The procedure allows the gas temperature to be deter-mined directly from the measured signals with little or

2150 APPLIED OPTICS / Vol. 28, No. 11 1 June 1989

no a priori information concerning the character of theabsorption or scattering.

II. Experimental Facility

A series of emission-absorption pyrometer measure-ments were made on a bench top burner with thecombustion gases seeded with scattering particles.We have concentrated on conditions in which second-ary corrections, i.e., the effect of wall emission and theeffect of unequal gas and particle temperatures, can beconsidered negligible. This was done to test carefullythe basic correction given in part 1l of this paper.

To test the measurement algorithm outlined above,a series of experiments were performed on a benchtopflat flame combustor. The surface of the combustor isan 8.9 X 2.5 cm area composed of over 200 diffusionflames in close-spaced array. The diffusion flame de-sign was selected to allow hydrogen and/or carbonmonoxide to be burned in pure oxygen. Measuredflame temperatures up to 3000 K have been achievedwith these reactants. As a seed material, potassiummetal is vaporized into nitrogen carrier gas and fed tothe burner surface with the fuel. The reactants maybe heated up to 4500C and the burner body to 5500 C.In this manner stable seed concentrations of over 1%by mass in the flame have been obtained. Not only isfeeding the seed as a vapor very stable in time but theconcentration is accurately controllable by varying thecarrier flowrate and the liquid metal temperature. Anaerosol of powdered ceramic (here, high purity alumi-na) is generated from a fluidized bed. This is admixedwith the oxidizer to introduce scattering particles intothe flame. This benchtop burner was designed tosimulate combustion MHD plasma conditions at lowvelocity and thermal power (10 kW).

To minimize heat losses and shield the flame fromentrained room air, the burner is equipped with awater-cooled chimney lined with a double layer of alu-mina or magnesia brick. Removable ports are provid-ed in all four sides of the chimney to allow access to thefirst 5 cm of the gas above the burner surface. Opticalaccess is made by replacing these ports with onesequipped with nitrogen-purged quartz windows. Theburner is built into the center of an optical breadboardwhich forms the top of a portable stand containing allthe support equipment.

To minimize the effects of unequal gas and particletemperature we chose aluminum oxide for the scatter-ing particles since the ratio of the absorption to scat-tering cross section is very small at 766.5 nm. Theradiative properties of alumina particles will be dis-cussed more fully below. The effects of emission fromthe chimney ceramic liner are minimal for the case athand. The liner wall temperature, which was mea-sured to be -1600 K, is so much lower than the gastemperature that the blackbody radiance of the wallsis negligible compared to that of the gas.

The optical system used for these experiments isshown schematically in Fig. 1. The emission-absorp-tion pyrometer, described in detail by Paul,2 3 incorpo-rates many new features extending its capability and

Figure 1. Schematic of the emission-absorption pyrometer opticalsystem (AS-aperture stop, B-beamsplitter, C-chopper, DE-signal demultiplexer, D-detector, F-filter, L-reference lamp,

M-mirror, P-pyrometer, PS-power supply).

minimizing several potential sources of error. Thereference source L is a subminiature quartz-halogenlamp. Radiation from the reference source is lenscoupled in two 1 mm step index optical fibers formingthe reference and measurement paths. Magnified im-ages of the ends of these fibers are imaged into thecenters of the flow channel and a dummy channel forthe reference path, respectively. A demagnified im-age is then formed at the end of the receiving fibers.To insure that only gas illuminated by the source isseen by the receiver, the receiving fiber is of smallerdiameter (0.6 mm) than the transmitting fiber. Anaperture stop is used in conjunction with the smallerfiber to guarantee that the solid angle for reception isless than that for illumination.

The reference path is generated from the samesource as the signal path, which obviates the need for asecond calibrated lamp. This eliminates problemsdue to relative drift if two lamps are used. In thereference path, provision is made to periodically moni-tor the lamp brightness temperature via mirror M anda standard calibrated pyrometer P. Any minor differ-ence in signal level between the two paths, in theabsence of the hot gas, is balanced by adjusting thereference path aperture stop or the amplifier gains inthe electronics. The dummy channel optics aremounted on x-y-z translation stages to give some flexi-bility to simulate the measurement optics at the flowchannel.

The signals from the reference and measurementpaths are combined in a cube beam splitter B to form atriply multiplexed optical signal. The signals are se-quenced via the synchronized miniature choppers C1and C2. This allows for two detector-filter combina-tions, and, by utilizing additional beamsplitters, thenumber of simultaneous measurement wavelengths iseasily increased to three or four. The radiation in eachchannel is spectrally filtered (F1,F2, . . .) and receivedby silicon photodiodes (D1,D2, ... ).

1 June 1989 / Vol. 28, No. 11 / APPLIED OPTICS 2151

The spectral selection filter elements are narrowband interference filters, or Fabry-Perot etalons tunedby tilting or piezo-electric adjustment, respectively.Because of the high seed concentration used here, thepotassium resonance lines are very broad (transferbroadened to -5 nm FWHM), thus interference filtersare appropriate. For more conventional combustionsystems, where weak sodium seeding would give a nar-row line, an air-spaced thermally stabilized Fabry-Perot etalon would be employed. The measurementsreported here were performed using two-cavity inter-ference filters with a FWHM of 0.3 nm and 55% peaktransmission which are conveniently tuned by rotationthrough a small angle to the optical axis.

This instrument has been extensively tested2 3 on apurely absorbing gas. The temperature measurementresolution is better than one Kelvin at a temporalresolution of 1 ins. The instrument can be calibratedto obtain an absolute error of better than 10 K in 3000K. This absolute error is primarily due to the errorsassociated with the available spectral emissivity dataof tungsten required to correct the reference sourcebrightness temperature2 for wavelengths of operationother than the NBS standard of 655 nm.

Ill. Experimental Results

Measurements of SG, SL, and SG+L were made simul-taneously at three wavelengths using interference fil-ters. Measurements were made at a fixed potassiumseed concentration of 0.03% by mass in a stoichiomet-ric hydrogen-oxygen flame. The level of potassiumseeding used here was selected so as to obtain largevalues of the total albedo in the wings of a potassiumresonance line.

The particles were introduced into the flame byfluidizing a fine alumina powder in with the oxidizer.The powder used in these experiments was a highpurity, fused, a-phase alumina commercially availableas an optical abrasive. The particle concentration wascontrolled by bypassing only a portion of the oxidizerthrough the fluidized bed. Though not required forthe particle scattering corrections, the particle concen-tration and size distribution were measured in theburner chimney under cold flow conditions. This wasdone to determine the particle feeder's stability in timeand the feed uniformity of the particle flux over theburner surface. This information was also used forestimating the magnitude of the scattering correctionvia a Mie scattering calculation. A Climet model 208Aoptical-size analyzer equipped with a 100:1 predilutionsystem in conjunction with a TSI model 3030 electricaerosol analyzer were employed to make these mea-surements. The Climet analyzer operates over a rangeof 0.3 to 10 ,qm and the electric aerosol analyzer oper-ates over a range of 0.01 to 1 um. To sample theparticle laden flow, a pair of isokinetic probes wereinserted down the chimney to -3 cm above the burnersurface.

It was found that the fluidized bed can deliver anaerosol with a loading of -5 X 104 particles per cubiccentimeter to the burner surface. At higher feed rates

1.0

0.8

:00,

*0

C

0.6

0.4

0.2

0.0

10-2 1o1 101

Particle Diameter (microns)

Figure 2. Measured particle-size distribution.

the bed becomes unstable. It was also found necessaryto condition the bed by fluidizing the particles for -/2hour. This procedure was required to remove the veryfine, highly mobile particles to obtain a stable' sizedistribution. A plot of the typical particle size distri-bution is shown in Fig. 2.

An advantage of using alumina as a seed material isthat its optical properties have been widely studied athigh temperatures for both the bulk solid and particleform. It is generally accepted4'5 that the real part ofthe refractive index is a very weak function of tempera-ture and wavelength in the visible. The value is takento be that of synthetic sapphire reported by Malitson.6However, the imaginary part of the refractive index isfound to be a strong function of both temperature andwavelength in addition to being highly dependent onthe material phase and impurity content.7' 8 The val-ues reported by Mularez7 are appropriate for the parti-cles employed here, since they are for an a-phase alu-mina with a similar impurity content. Using thesedata for the complex refractive index (m = 1.77-0.0011i at 766 nm, 2550 K), a Mie scattering computationgave a ratio of the (particle distribution averaged)absorption to scattering cross sections of 0.0027 (or aparticle albedo of 0.997) at 766 nm. Further, it followsthat the particle emittance is very small; thus, with asmall radiative heat loss, the particle temperature isessentially that of the gas. This suggests that there isno need to correct for particle emittance since TG TPand since axp/a). << 1.

Since the particle radiative properties are essential-ly constant over the wavelength range of the experi-ment (3.5 nm), changes in the albedo and opticaldepth are solely due to the strong wavelength depen-dence of the absorbing gas species (here the 766.5 nmresonance line of potassium). Since the potassiumabsorption dominates the radiative transfer, the albe-do tends to zero at line center. However, in the linewings, the albedo tends to unity as the gas absorptionbecomes less and less important. That is actually veryfortunate because it allows the true gas temperature tobe measured without the need for a scattering correc-tion. This can be done simply by employing the emis-

2152 APPLIED OPTICS / Vol. 28, No. 11 / 1 June 1989

- A Electric Aerosol Analyzer

- * Climet Analyzer

At\

X\ *! t g g g | a s ! _ .X-

L E 3 ,D U,9 0 CDE3s3[ Q

Oa~os AN ffi QEl] [lag

0 D() c D Wd 65

0.0

2'

C_a)

-n5

a.)C

0EIa,

-25.0

-50.0

'_.05 0.5 5.0Total Optical Depth

Figure 3. Measured temperature using different levels of correc-tion to account for the effects of scattering.

sion-absorption pyrometer at large optical depths andreducing the data via Eqs. (6 and 7) (the algorithm for apurely absorbing gas). This is only possible becausethe benchtop burner employs an unseeded burningshroud flame and thus does not exhibit any self-rever-sal at line center. Measurements made in the wings ofthe spectral line which require the scattering correc-tion could then be directly compared to the true, mea-sured gas temperature.

In Fig. 3 the gas temperature (as a function of mea-sured total optical depth) is shown, calculated from themeasured signals, by assuming: (1) a purely absorbinggas; (2) a zeroth-order scattering correction (Tho-mas's9 method); (3) an isotropic first-order scatteringcorrection; and (4), an anisotropic first-order scatter-ing correction. These results are plotted as differ-ences from the gas temperature measured at line cen-ter using the algorithm for a purely absorbing gas.The measurements reported here are the average of a512-point sample, which was used to enhance the in-strument signal to noise and thus allow precise mea-surements to be made at small values of the totaloptical depth. Since the scattering corrections re-quire two measurement wavelengths we have adoptedthe convention of plotting these results as a function ofthe larger of the two total optical depths (xl).

As expected all of the methods asymptotically mea-sure essentially the same value of the gas temperatureat large optical depths. This is due to the strong gasabsorption at line center which reduces the total albe-do and hence produces a reduction in the magnitude ofthe scattering correction.

In Fig. 3, the error incurred by assuming a purelyabsorbing gas is very pronounced at small opticaldepths, becoming more than 100 K at Fx = 0.1. Thisis due to the increase in the total albedo in the line

0.6 -

0

0 0.4 _

0.2 -

0.0 A.05 0.5

Total Optical Depth5.0

Figure 4. Measured total albedo.

wings. The error can be simply estimated in terms ofthe zeroth-order correction by

ATG [ C I 1-'TG L XTG J (9)

Since the total albedo is bounded by the range 0 < wX <1, the overall sign of the error is negative. Thus, as thealbedo increases, the measured gas temperature fallsoff rapidly from the true gas temperature. Function-ally, the effect of completely neglecting scattering is toequate the total extinction coefficient to the total ab-sorption coefficient. This results in overpredictingthe gas emittance which in turn results in a low mea-sured gas temperature.

The use of the zeroth-order correction (i.e., Tho-mas's 9 method) shows a marked improvement overneglecting scattering altogether. Since this methoduses only the zeroth-order term in the series solution ofthe equation of transfer, the effect is to underpredictthe gas emittance and consequently to measure a high-er gas temperature. The measurement error in com-parison to the first-order isotropic method can be esti-mated by the relation

AT, 1 C2 A'0(r,)TG [ XTG/\ + [1 -exp(-rF)]f)J(10)

where the quantity A' is defined in part 1.1 Since thesecond term in the denominator is greater than unity,the overall sign of the error is positive. The zeroth-order method does provide a measure of the total albe-do which is shown in Fig. 4. It is interesting to notethat the albedo measured using the zeroth-order meth-od agrees remarkably well with that measured usingthe higher-order methods yet to be discussed and alsoshown in this figure. Using the definitions of the total

1 June 1989 / Vol. 28, No. 11 / APPLIED OPTICS 2153

0

* No Correctiono Zeroth OrderA 1 st Order Isotropico 1st Order Anisotropic

I ' ' ' ' ' ' . . I . . . . . I . . I .

25.0 0.8

0o

1 , X,-75 .

5

0

-5

7a,a,0

C

5a

0.a

E

0

0

5

5

0

5

0

El 0bta CD0 0000 000 ED 0 00 0

a= 1.0

[770)0)D a 0E oo o 0 00 0

~0) 0 0 ~0 oa = 00

0

j I -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- 5 m~~~~a ffm a]z° 0° °9

a = 0.125

CM O 00 0

13zP b ra = 0.05nA0.50

05 T IO 5 I h5.0Total Optical Depth

Figure 5. The effect of assuming different particle mean radius onthe anisotropic first-order correction.

optical depth and the total albedo the scattering coeffi-cient can be obtained from these measurements as urA =

cwxr'/d, where d is the measurement pathlength. Thisgives a measured value of a, = 6.5 X 10-3 cm-1 which,within the uncertainty in the measurement of the par-ticle size distribution and loading, is consistent withthat given by a Mie scattering calculation using therefractive index data reported by Malitson6 and byMularez. 8 The value of A, inferred from the mea-sured values of wx and Ix, is very nearly constant over arange of two decades in total optical depth. This isconsistent with the expected behavior of the scatteringcoefficient for a particle distribution over a limitedwavelength range.

The gas temperature, as measured using the first-order method is shown in Fig. 3 both for isotropic andanisotropic scattering corrections. Although the par-ticle-averaged phase function expansion has over 40significant terms, the anisotropic correction used hereemploys only the first 12-14 terms. The series wastruncated when the value of A/A became less than10-8. The slight negative trend with decreasing opti-cal depth seen in the isotropic result is consistent withthe results of numerical simulations performed by Chuet al.10 Their results suggest that, for a finite slab, theassumption of isotropic scattering leads to an overpre-diction of gas emittance. As is the case when scatter-ing is altogether neglected, this leads to a low value ofmeasured gas temperature.

As is evident from Fig. 3, the performance of theanisotropic correction is excellent, given the a prioriknowledge of the particle size distribution and thecomplex refractive index of alumina. It is interestingto consider the sensitivity of the anisotropic correctionto some uncertainty in the particle properties. In Figs.5 (a), (b), (c), and (d), the results of the anisotropiccorrection as applied to the measured signals areshown assuming a refractive index of 1.75, a value of b

5

0

-5

5

a,

LI

CsE

a,

. _

E

0

-5

5

0

-5

5

0

-5

N = 2.0

eOn ma 03 a, 010oaoocn a o 0

N = 1.6

E) ao[u:m q]3 3OcioQ[0 oo° 0 ° 0

N = 1 .5

'''I

> 003 000 003 U00 C

N = 1 .3

.05 0.5Total Optical Depth

5.0

Figure 6. The effect of assuming different real refractive index forthe particles on the anisotropic first order correction.

= 0.1 and for values of a = 0.1, 0.25, 1.0, and 2.0,respectively. The parameters a and b are the effectivemean radius and the variance of the particle size distri-bution." In like fashion, the effect of assuming thereal portion of the refractive index to be n = 1.3, 1.5,1.6, and 2.0 is shown in Figs. 6 (a), (b), (c), and (d),respectively, for the actual particle size distributionused in these experiments.

From these figures we see that the measurementtechnique is reasonably insensitive to changes in thereal part of the refractive index over a range of 20%. Infact, most amorphous refractory oxides have values of1.5 < n < 1.9, in the visible spectrum. Further, weobserve that assuming greater mean particle sizes re-sults in almost no effect but the assumption of smallermean sizes gives a result similar to that obtained withthe isotropic correction. This is to be expected, sincefor a = 0.05 which gives a value of x 7rd/X z 0.85, thetrue angular scattering pattern is much more symmet-ric and better approximated by isotropic scattering.From the data tabulated by Chu, Clark and Church-ill,12 variation in the particle size and refractive indexover the ranges considered here do not significantlyeffect the overall size and shape of the forward portionof the phase function, which is of primary importanceto the anisotropic correction. Variations of the parti-cle properties over these ranges do, in fact, significant-ly effect the particle scattering and absorption coeffi-cients, but the scattering correction procedurepresented here effectively measure these data. Thuswe find that the anisotropic correction for temperaturemeasurement can effectively be applied with only typi-cal data on the particle refractive index and size distri-bution available.

The results of the scattering corrections, shown inFig. 3, are shown replotted in Figs. 7 (a), (b), and (c).Here the measurements were broken into groups forthe different values of R rx1/rX2 and were plotted as a

2154 APPLIED OPTICS / Vol. 28, No. 11 / 1 June 1989

-

-

2'

a)C)a,

51 st Order Isotropic

0 cC _ _ _ _ _ _ _ __10 1

o 1.25< R < 1.5o3l.5 < R <2.5

-5 A 2.5 < R < 3.50 3.5 <R<4.5

-10CC, Cl ,C C C C C ,, l

15TZeroth Order

10 0

5 aog

O. I'n ,,,1 0.5

Total Optical Depth5.0

Figure 7. The effect of differing ratios of the total optical depth ondiffering orders of the scattering correction.

function of rxj. In each case no significant depen-dence on the value of R can be observed. This isconvenient in that the choice of operating wavelengthsis not critical and is constrained only by prudent sig-nal-to-noise considerations. It should be noted thatfor values of R < 1.25 some difficulty associated withthe independence of the measured signals can be antic-ipated.

IV. Summary

The results obtained from the measurements madein an emitting, absorbing, and scattering medium con-firmed the need to correct for the effects of scatteringand the large potential error incurred by neglectingthese effects. The measurements reported here weremade under conditions of strong gas absorption and ofa particle albedo near unity. Hence, to see a signifi-cant difference between the zeroth-order and first-

order methods, it was necessary to consider the resultsfor total optical depths <0.1, in which case both meth-ods are expected to perform well. However, in situa-tions in which weak gas absorption combined with along measurement pathlength serves to yield large to-tal albedos at higher optical depths, it is expected thatthe use of first-order methods will be required to prop-erly account for scattering effects. The anisotropicfirst-order correction was found to provide superiorperformance while being quite insensitive to the exactparticle properties assumed.

References1. P. H. Paul and S. A. Self, "Method for Spectroradiometric

Temperature Measurements in Two Phase Flows. 1: Theory,"Appl. Opt. 28, 2143-2149 (1989).

2. P. H. Paul, "Spectroradiometric Temperature Measurements inTwo-Phase Combustion Plasmas," Doctoral Dissertation, Stan-ford U. (1984), HTGL report T-238.

3. P. H. Paul and S. A. Self, "The Use of Quartz-Halogen Lamps forSpectroradiometric Temperature Measurements," Rev. Sci. In-strum. 59, 260-264 (1988).

4. G. N. Plass, "Temperature Dependence of the Mie Scatteringand Absorption Cross Sections for Aluminum Oxide," Appl.Opt. 4, 1616-1619 (1965).

5. E. J. Mularez and M. C. Yuen, "An Experimental Investigationof Radiative Properties of Aluminum Oxide Particles," J.Quant. Spectrosc. Radiat. Transfer 12, 1553-1568 (1972).

6. I. H. Malitson, "Refraction and Dispersion of Synthetic Sap-phire," J. Opt. Soc. Am. 52, 1377-1379 (1962).

7. E. J. Mularez, "An Experimental Investigation of the RadiativeProperties of Solid and Molten Alumina," Doctoral Disserta-tion, Northwestern U. (1971).

8. J. M. Adams, "A Determination of the Emissive Properties of aCloud of Molten Alumina Particles," J. Quant. Spectrosc. Ra-diat. Transfer 7, 273-277 (1967).

9. D. L. Thomas, "Problems in Applying the Line Reversal Methodof Temperature Measurement to Flames," Combust. Flame 12,541-549 (1968).

10. C. M. Chu, J. A. Leacock, J. C. Chen, and S. W. Churchill,"Numerical Solutions for Multiple, Anisotropic Scattering,"Electromagnetic Waves V5, Proceedings of the Interdisciplin-ary Conference on Electromagnetic Waves, M. Kerker, Ed.(Plenum, New York, 1963).

11. E. H. Hansen and L. D. Travis, "Light Scattering in PlanetaryAtmospheres," Space Sci. Revs. 16, 527-610 (1974).

12. C. M. Chu, G. C. Clark, and S. W. Churchill, "Tables of AngularDistribution Coefficients for Light-Scattering by Spheres," En-gineering Research Institute Report (U. Michigan P., Ann Ar-bor, MI, 1957).

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