emission

Soot Pyrometry using Modulated Absorption/Emission T. P. JENKINS* and R. K. HANSON

Department of Mechanical Engineering, Stanford University, Palo Alto, CA USA A new method of optical pyrometry for sooting flames has been developed that combines absorption and emission measurements at the same wavelength, reducing the uncertainty in measured soot temperature when compared to commonly used two-color emission pyrometry. The new technique, modulated absorption/ emission (MAE) pyrometry, utilizes combined emission and absorption at two wavelengths: 830 and 1300 nm. Large uncertainties in the wavelength-dependent soot refractive index in the infrared are avoided by measuring emissivity directly, eliminating the need to rely on a refractive index model when obtaining temperature. One-color and two-color MAE techniques are validated in this study in a rich laminar premixed ethylene/air flame using diode lasers for transmission measurements. The results show a reduction in the uncertainty of measured temperature in an example case from greater than ⫾50 K with conventional emission-only pryometry to ⫾20 K with MAE pyrometry. Advantages of MAE over the conventional method are greatest for soot volume fractions on the order of 10⫺7 or greater, typical of laboratory flames used in soot formation and growth studies. © 2001 by The Combustion Institute

INTRODUCTION Optical pyometry is an attractive technique for measurements of temperature and soot volume fraction in flames since it is non-intrusive and offers rapid time response. Two-color pyrometry has been widely used for fundamental studies of both laminar and turbulent flames [1–7] as well as for studies of practical devices, such as diesel engines [8 –10]. The method employs measurements of visible or infrared emission from soot at two wavelengths. Planck’s blackbody function is used, together with a model for the emissivity of the soot, to relate measurements of emission intensity at the two wavelengths to temperature and soot volume fraction. Accuracy can be significantly limited by the uncertainty in the emissivity model, which may be based on the wavelength-dependent refractive index of soot. Experimental difficulties associated with measuring soot refractive index have resulted in substantial scatter in the data. Dyer and Flower [11] introduced an alternative form of pyrometry using a modulated light source for transmission that combines measurements of emissivity and emission intensity at the same wavelength along a common path, eliminating the need for assuming a re* Corresponding author. E-mail: tjenkins@metrolaserinc. com Current Address: MetroLaser, 18010 Skypark Circle, Suite 100, Irvine, CA 92614-6428. COMBUSTION AND FLAME 126:1669 –1679 (2001) © 2001 by The Combustion Institute Published by Elsevier Science Inc.

fractive index to obtain temperature. However, the technique is not widely used, perhaps because of the lack of available light sources at wavelengths of strong emission. The present study shows how this technique can be applied using recently available infrared diode lasers and fiber optics, and demonstrates that this new diagnostic offers an improvement in accuracy of temperature measurements over conventional two-color emission pyrometry. Optical pyrometry techniques have some limitations. Typically, emission measurements are collected along a path extending through the flame. The resulting lack of spatial resolution implies that such methods are best suited for flames with homogeneous temperature distributions. Variations in temperature cause measurements to be biased toward the hotter regions, due to the T4 dependency of emitted radiation. Soot volume fractions obtained from emission measurements thus tend to be lower than from absorption measurements, since the colder soot is unaccounted for. Also, because emission is typically collected at visible wavelengths, intensity is low at temperatures less than about 1200 K, limiting the technique to relatively high temperatures. Despite these shortcomings, optical pyrometry has found widespread use in the study of diesel engines, as evidenced in SAE papers [8 –10], perhaps at least in part because the highest temperatures are often the ones of most interest for the control of pollutants. A sensitivity study of two-color pyrometry was 0010-2180/01/$–see front matter PII 0010-2180(01)00278-4

1670 conducted by di Stasio and Massoli [12] in which it was found that larger uncertainties in both soot temperature and soot volume fraction resulted when infrared wavelengths were used rather than visible. For wavelengths greater than 800 nm, they estimated uncertainties in soot temperature to be greater than 200 K for soot volume fraction (fv) on the order of 10⫺7, and ⬎80 K for fv on the order of 10⫺5. They also concluded that the two-color technique in any range of wavelengths is “severely hampered” for small fv, i.e., on the order of 10⫺7 or less. The large uncertainties are due mostly to the high sensitivity of the technique to the optical constants in the infrared: a result of Plank’s function. This is unfortunate for two reasons; first, if it weren’t for the greater sensitivity to emissivity, infrared wavelengths would be preferred since most of the radiation from soot at flame temperatures is in the infrared, leading to higher signal to noise ratios. Second, compared to visible wavelengths, infrared wavelengths make it easier for the Rayleigh criterion to be met, i.e., that the wavelength be significantly longer than the characteristic soot particle diameter. Thus, a method that reduces uncertainty in the emissivity in the infrared is desirable. The study of di Stasio and Massoli [12] suggests that visible wavelengths are to be preferred in two-color soot pyrometry. However, their study is based mainly on uncertainties stemming from the refractive index model, and does not take into account the reduction in emission at visible wavelengths. Whereas in the infrared the overall uncertainty in temperature is dominated by the emissivity, in the visible it may be dominated by the emission intensity, and thus by detector noise. The reduced emission signal at visible wavelengths can lead to uncertainties on the same order as those that they calculated for infrared wavelengths. For example, in our laboratory a silicon photodiode detector was used to measure emission from a sooting flame (fv ⫽ 8 ⫻ 10⫺8) at 650 nm with a 40 nm bandwidth filter, resulting in a signal to noise ratio of 16:1. This was the dominant uncertainty in the temperature obtained using a conventional two-color method, with the other wavelength being 830 nm, resulting in a temperature uncertainty of over 80 K. A soot temper-

T. P. JENKINS AND R. K. HANSON ature diagnostic with better accuracy is clearly desirable, and as shown in the following sections, can be obtained using combined emission and absorption measurements at infrared wavelengths. Gore and coworkers [1– 4] developed a pyrometry method using a probe that collected simultaneous emission measurements at 800 and 900 nm and extinction measurements at 632 nm. They used this probe in studies of jet flames and various types of pool fires to obtain data on the turbulence characteristics of temperature and soot volume fraction. Like most two-color pyrometry techniques, their probe did not measure emission and extinction simultaneously at the same wavelength, so they had to rely on a model of the soot refractive index to obtain temperature. Here we identify four models of refractive index that are in common use [13–16], and which differ significantly from one another. The availability of low-cost diode lasers in a wide range of visible and infrared wavelengths makes it practical to combine measurements of laser extinction and flame emission in a pyrometer capable of soot temperature measurements with high accuracy, even when soot concentrations are relatively low, on the order of 10⫺7 (0.1 ppm). Following this concept, a new pyrometer was developed and tested that measures both laser transmission and soot emission intensity at both 830 and 1300 nm. This pyrometer has the advantage that a more accurate determination of emissivity is possible than for conventional pyrometry methods, which rely on questionable models. In the present work, we first review the theory of conventional two-color pyrometry, and then introduce MAE pyrometry. Next, we describe the experiment used to validate the MAE techniques, and finally we present the results from these experiments, and discuss their significance. THEORY Conventional Two-Color Methods Optical pyrometry methods in sooting flames involve the measurement of soot temperature using the relation:

SOOT PYROMETRY BY USING MAE

1671

J␭(T) ⫽ ⑀␭J␭bb(T)

(1)

where J␭(T) is the measured monochromatic emission intensity primarily from soot, ⑀␭ is the soot emissivity and J␭bb(T) is the black-body emission, given by Planck’s formula: J ␭bb ⫽

␭

C1 C2 exp ⫺1 ␭T

再 冉 冊 冎

5

(2)

where C1 and C2 are constants. There are two models for emissivity in common use. The first is given by Hottel and Broughton [17], which is:

冉 冊

⑀ ␭ ⫽ 1 ⫺ exp ⫺

KL ␭␣

(3)

where K is a wavelength independent factor proportional to soot concentration, L is the optical path length, and ␣ is an empirical con-

冦

冉 冉 冊 冊

C2 exp ⫺1 ␭ 1T J1 C1

␭ 51 1⫺

␭␣1 1

冧 冦

冉 冉 冊 冊

␭ 52

⫽ 1⫺

冉

F␭ f L ␭ v

冊

(5)

where

冦

冉 冉 冊 冊

␭ 51 1⫺

␭1 F1

冧 冦

C2 exp ⫺1 ␭ 1T J1 C1

⫽ 1⫺

F␭ ⫽

(4)

(6)

where fv is the soot volume fraction, and n and k are the real and imaginary parts, respectively, of the soot refractive index, n ⫺ ik, and are dependent on wavelength. This approach assumes that the soot particles are small enough to meet the requirement 2␲r/␭ ⬍ 0.3. Substituting Eq. (5) and (2) into (1), solving for fvL for each of two wavelengths, and equating, we get:

冧

C2 exp ⫺1 ␭ 2T J2 C1

which was also solved by iteration to yield T in the present study. F1 and F2 were specified using an assumed index of refraction for each wavelength. Gore and co-workers [1– 4] have used this approach extensively with wavelengths of 900 and 1000 nm using the refractive index model of Dalzell and Sarofim [13]. The present

␭␣2 2

36 ␲ nk 共n 2 ⫺ k 2 ⫹ 2兲 2 ⫹ 4n 2k 2

冉 冉 冊 冊

␭ 52

冧

C2 exp ⫺1 ␭ 2T J2 C1

where the measured intensities J1 and J2 yield T for assumed values of ␣1 and ␣2. In the present study, Eq. (4) was solved for T by iteration using ␣1 ⫽ ␣2 ⫽ 0.95. In the second approach, emissivity is modeled by using Rayleigh theory as (e.g., [19] or [20]):

⑀ ␭ ⫽ 1 ⫺ exp ⫺

stant. Hottel and Broughton [17] measured ␣ to be 1.39 for visible wavelengths and 0.95 for the infrared. Liebert and Hibbard [18] also measured values of ␣ experimentally and found ␣ ⫽ 0.95 ⫾ 0.1 with no dependence on wavelength in the range 0.4 ⬍ ␭ ⬍ 5 ␮m. The difference in the recommended values of ␣ among these two research groups reflects the problems faced in applying the optical properties of soot measured in one experiment to pyrometry in another experiment. The cause for the differences is unknown, and may be inaccuracies in the measurements of ␣, or differences in the optical properties of the soot produced by the two flames. In conventional two-color pyrometry, Eqs. (2) and (3) are substituted into Eq. (1), and the result is solved for KL. This is done for each of two wavelengths (␭1 and ␭2), and the results are equated to each other, giving:

␭2 F2

(7)

work employs wavelengths that are more widely separated, 830 and 1300 nm, giving better temperature sensitivity. In the present work, four models of refractive index were employed, each producing a different result. The models used were from Dalzell and Sarofim [13], Lee and Tien [14], Habib and Versisch [15], and Chang

1672 and Charalampopulous [16]. Once T was obtained, fv was calculated by combining Eqs. (1), (2), and (5). Throughout this paper, the methods using Eqs. (4) and (7) are referred to as the ␣ and F algorithms, respectively. A sensitivity study was done following the methods of Wang et al. [21] to determine the optimum wavelength pair. Briefly, Planck’s formula was used to determine the ratio of emission intensities at two wavelengths as a function of temperarure. The derivative of this ratio with respect to temperature, labeled the “sensitivity,” was used as the criterion for optimization. The wavelength pair was selected such that the sensitivity was maximized over the temperature range 1200 to 5000 K, resulting in wavelengths of 830 and 1300 nm. This range of temperatures is high for typical soot studies. However, it was selected based on the application that originally motivated the development of this diagnostic: a pulse detonation engine. The MAE method proved to be a useful diagnostic for soot temperature and volume fraction in a pulse detonation engine [22]. Additional considerations included selecting wavelengths that were far from any gas bands expected in the combustion products. Calculated absorption spectra for the major product species (H2O, CO2, CO, and OH) revealed an absence of strong absorption near 1300 nm, with the nearest strong absorber being from H2O at ⬃1400 nm. One-Color MAE Pyrometry One-color MAE pyrometry is based on a method first used by Dyer and Flower [11], in which a white-light source was used for transmission measurements, modulated with a chopper wheel. Modulation frequencies were significantly higher than the frequencies associated with combustion, thereby enabling the separation of emission and extinction measurements at the same wavelength by using a single detector. In the present adaptation of the method, we make use of a diode laser as the light source to improve the spectral and spatial resolution, and use acousto-optic modulation to extend the potential bandwidth into the megahertz range.

T. P. JENKINS AND R. K. HANSON Like the conventional two-color method, the MAE method assumes that the soot particles are small enough that scattering is insignificant compared to absorption. This assumption has been shown to be valid in the luminous region of similar laminar flat flames [23–25]. Therefore, the fraction of light absorbed (absorbance) by soot particles along a path through such a flame is equal to 1 ⫺ ␶␭, where ␶␭ is the fraction transmitted. Kirchhoff’s law states that the directional spectral emissivity of a material, ⑀␭, is equal to the directional spectral absorbance [20]. Thus:

⑀ ␭ ⫽ absorbance ⫽ 1 ⫺ ␶␭

(8)

and a measurement of ␶␭ yields ⑀␭. Substituting Eq. (2) into Eq. (1) gives. J␭ ⫽

␭

⑀ ␭C 1 . C2 exp ⫺1 ␭T

再 冉 冊 冎

5

(9)

Substituting Eq. (8) into Eq. (9), and solving for T, we have: T⫽

C2 . 共1 ⫺ ␶ ␭兲C 1 ␭ ln ⫹1 J␭ ␭5

冉

冊

(10)

Equation (10) yields T from measurements of J␭ and ␶␭. Soot volume fraction can be obtained from ␶␭ in the conventional way; Eq. (8) substituted into Eq. (5) yields fv from ␶␭. In the present experiment, a laser was used as the light source, modulated with a square wave pattern at 1 kHz. Time histories of emission intensity from flames used in the present study showed that significant oscillations were not apparent above 20 Hz. Therefore, the 1-kHz modulation frequency was high enough that there was negligible change in the flame properties between consecutive modulation cycles, and thus emission and transmission could effectively be measured together within one cycle of modulation. During each laser-off interval, a measurement of emission intensity was made, while a corresponding measurement of laser transmission was made during the next laser-on interval.

SOOT PYROMETRY BY USING MAE

1673

Fig. 1. Arrangement of optical components for validation of a new soot pyrometry technique combining measurements of modulated laser absorption with flame emission.

Two-color MAE Method Combining emission and absorption measurements at two wavelengths leads to yet another way to determine soot temperature. When exp(C2/␭T) ⬎⬎ 1, the denominator in Eq. (9) can be approximated by exp(C2/␭T). This approximation is valid for ␭T ⬍ 3000 ␮m K [12], a condition that is met for the wavelengths in the current study, 830 and 1300 nm, for temperatures less than 3600 and 2300 K, respectively. We may write Eq. (9) for each of two wavelengths, ␭1 and ␭2, divide one equation by the other, and solve for T. Using the approximation for exp(C2/␭T) ⬎⬎ 1, the result is:

冉

冊

1 1 ⫺ ␭2 ␭1 , T⫽ J1 ␭1 5 ⑀2 ln J2 ␭2 ⑀1 C2

再 冉冊 冎

(11)

where the ratio of emissivities, ⑀2/⑀1, and the ratio of intensities, J1/J2, are measured quantities. This method has an advantage over the one-color method of Eq. (10); only the ratio of emission intensities needs to be measured, not the absolute magnitudes, so that errors incurred from any uncertainty in the solid angle of col-

lection are avoided. This feature may be especially important if the solid angle is different for the calibration than for the flame measurements, which was the case here. EXPERIMENTAL Figure 1 shows the optics arrangement for validation experiments that were conducted in a laminar premixed flat flame. A McKenna burner was employed to produce a rich ethylene/air flame that was uniform in the horizontal plane. Premixed fuel and air issued from a 60-mm diameter porous disk that was surrounded by a nitrogen co flow issuing from a 6-mm-wide annular region. A steel wire screen placed 23 mm above the burner surface stabilized the flame. Experiments were conducted with fuel/air equivalence ratios, ␾, between 2.1 and 2.4, where ␾ is defined as:

␾⫽

F/A 共F/A兲 st

(12)

where F/A is the fuel-to-air mass ratio, and the subscript st indicates stoichiometric conditions. Measurements were made in the luminous

1674 region containing soot particles, at a location 14.5 mm above the burner surface. Emission from the flame was collected along a path ⬃5 mm in diameter into a 1000-␮m fiber, as shown in Fig. 1. This arrangement resulted in a path length of ⬃60 mm. The light exiting the fiber at the other end was collimated by a lens and separated into two beams by a beamsplitter. One of the beams was directed through an 830-nm filter with a 40-nm bandwidth, onto a Si photodiode detector. The other beam was directed through a 1300-nm filter with a 75-nm bandwidth, onto a InGaAs photodiode detector (Electro-Optical Systems, Inc., Phoenixville, PA). Signals from the detectors were digitized with 12-bit resolution at a rate of 100 kHz using a Nicolet digital oscilloscope (Nicolet Biomedical, Madison, WI, USA). During each experimental run, 8000 values were stored for each of the two wavelengths. The same detection system used for monitoring flame emission was used for monitoring transmitted laser light. Beams from two diode lasers were combined into a multimode 250 ␮m fiber using a grating, as shown in Fig. 1. The laser powers were ⬃1 and 0.5 mW at the measurement location with wavelengths of 829 and 1304 nm, respectively. Each beam was modulated at 1 kHz with an acousto-optic modulator for the present experiments, but could be modulated at up to 1 MHz for more rapidly changing flows. The modulators caused the intensity of each beam to vary with a square wave, on/off, pattern. Where the beams exited the fiber, they were projected by a lens into a collimated path through the flame, ⬃1 mm in diameter, that was co-linear with the path of emission collected by the 1000-␮m fiber. With this arrangement, the transmitted laser intensities at 829 and 1304 nm were combined with measurements of flame emission at essentially the same two wavelengths. The system of collection optics was calibrated by placing a tungsten filament lamp within the collimated collection path. A Minolta/Land Cyclops 152 optical pyrometer (Land Infrared, Newtown, PA) was used as a standard to measure the temperature of the tungsten filament. The emissivity of tungsten as a function of temperature and wavelength was obtained from Latyev et al. [26]. Signal levels from each of the

T. P. JENKINS AND R. K. HANSON two detectors were recorded for filament temperatures ranging from 1000 to 2000 K. For each of the two wavelengths, 830 and 1300 nm, the detector signal, when divided by the emissivity of tungsten, was observed to be proportional to the black body intensity calculated at the filament temperature, verifying the suitability of the source as a black body. Calibration constants X1 and X2 were obtained, such that J1 ⫽ V1/X1, and J2 ⫽ V2/X2, where J1 and J2 are the radiant intensities within the collimated collection path, and V1 and V2 are the voltages from the detectors. The filament was a ribbon 3 mm wide, so it did not completely fill the 5-mm diameter collection path that was filled by radiating soot during flame emission measurements. To correct for this, the calibration constants were multiplied by the ratio of the cross-sectional area of the collection path to the area of the filament intercepted by the collection path. A type-S thermocouple was used to measure flame temperatures at several locations across the diameter of the burner, at the same height above the burner surface as in the optical measurements. Thermocouple measurements in flames are typically subject to errors caused by conduction along the thermocouple leads, catalytic reactions on the thermocouple bead surface, and radiation loss to the surroundings. Conduction losses can be made insignificant by aligning the leads along the direction of the flame surface, so that there is minimal temperature gradient near the bead. In the present measurements, the leads were oriented parallel to the flame surface for a length of at least 40 wire diameters, so conduction errors should be less than a few degrees C. Catalytic reactions on the bead are of concern only near the flame zone, where the radical concentration is high. In the flames investigated in the current study, a light blue zone was apparent in the shape of a horizontal disk spanning the diameter of the burner located about 2 mm above the burner surface and less than 1 mm thick. This blue color is produced by band emission from radicals, primarily C2 and CH, and thus marks the flame zone where radical concentrations are high. All of the thermocouple measurements in the this study were performed far away from this flame zone, at a height of 14.5 mm above

SOOT PYROMETRY BY USING MAE the burner surface, thus catalytic reactions on the bead were considered not to be important. Corrections for radiation loss can be made if the bead size, shape, and emissivity are known. The emissivity of a bead surface depends upon its material, its surface texture, and its temperature. Typical values of the emissivity of a type-S thermocouple in a flame are from 0.20 to 0.30 [27, 28]. In the present study, a value of 0.25 was assumed. The bead shape was assumed to be spherical, with a diameter equal to 150 ␮m, which is twice the wire diameter. The correction involved an energy balance between convection and radiation [29] in which the convection was characterized by a Nusselt number of 2.0, the value for a sphere at very low Reynolds numbers. Calculated radiation corrections were temperature dependent, and ranged from ⬃50 to 65 K. The uncertainty in these corrections was estimated to be 25 K, with 15 K of the contribution coming from the uncertainty in bead emissivity, and 10 K from the uncertainty in bead size and shape. Thermocouple measurements in sooting flames may be complicated by soot accumulating on the bead during measurements. The presence of soot on the bead surface increases the emissivity, thereby increasing the radiative heat loss and lowering the apparent temperature. In the present thermocouple measurements, soot accumulation on the bead resulted in a steady reduction in the indicated temperature with time after insertion into the flame. The rate of reduction could be used to extrapolate back to zero time to approximate the correct temperature. This was done in the present measurements, with an estimated error due to extrapolation of 20 K. Thus, the overall uncertainty in the thermocouple measurements is estimated to be between 55 and 70 K, depending on temperature. RESULTS Data from the 830-nm detector during a typical experimental run are shown in Fig. 2. The dotted line indicates a reference signal obtained from measurements with no flame. Drift in the laser intensity was less than 0.5% for each laser during each experimental run, and was ⬃1.0%

1675

Fig. 2. Intensity of modulated laser light at 830 nm transmitted through a premixed ethylene/air flame, combined with flame emission. ␾ ⫽ 2.29, height ⫽ 14.5 mm. T ⫽ 1580 K.

from run to run. Thus, data with no flame were taken before a flame run, and were used for obtaining reference intensities. The modulator was not capable of totally blocking the laser, so a low-intensity laser signal appears during the “laser-off” part of the cycle. As depicted in Fig. 2, there are four measured quantities obtained for each cycle of modulation, which are 1) I0: the laser intensity during “laser-on” with no flame; 2) S ⫽ I ⫹ J: the transmitted laser intensity (I) and flame emission (J) during “laser-on;” 3) S⬘ ⫽ I⬘ ⫹ J: the transmitted laser intensity (I⬘) and flame emission (J) during “laser-off;” and 4) I⬘0: the laser intensity during “laser-off” with no flame. Although all quantities are wavelength dependent, the ␭ subscripts have been dropped for simplicity. The transmittance for a cycle can be written either as ␶ ⫽ I/I0:

␶ ⫽ I/I 0

(13)

or, equivalently, as:

␶ ⫽ I⬘/I⬘ 0

(14)

In order to write ␶ in terms of measurable quantities, we multiply both the numerator and denominator of Eq. (13) by the factor (1 ⫺ I⬘0/I0) and substitute I⬘/I⬘0 for I/I0 in the numerator, resulting in:

␶ ⫽ 共I ⫺ I⬘兲/共I 0 ⫺ I⬘ 0兲

(15)

1676

T. P. JENKINS AND R. K. HANSON

Fig. 3. Comparison of soot temperatures in a premixed ethylene/air flame calculated from emission and absorption measurements from the same data using five methods. The refractive indexes used for the F and ␣ algorithm methods were obtained from the model of Dalzell and Sarofim [13]. ␾ ⫽ 2.29, height ⫽ 14.5 mm.

Noting that the numerator in Eq. (15) is equal to (S ⫺ S⬘), we make this substitution and then substitute the result into Eq. (8), obtaining:

⑀ ⫽ 1 ⫺ 共S ⫺ S⬘兲/共I 0 ⫺ I⬘ 0兲

(16)

Once ⑀ was obtained, J was obtained by substituting Eq. (8) solved for ␶ into Eq. (14), then substituting the result solved for I⬘ into J ⫽ S⬘ ⫺ I⬘, resulting in: J ⫽ S⬘ ⫺ 共1 ⫺ ⑀ 兲I⬘ 0

(17)

Equations (16) and (17) were used to obtain both the emissivity and the emission intensity during each laser modulation cycle from the measured quantities. The data from the 1300-nm detector were processed the same way. A program written in FORTRAN extracted a time series of laser-on and corresponding laseroff values from the data. Soot temperatures for each run were computed by five different methods, using the same data set for each method. The methods were: a) two-color (830 and 1300 nm) pyrometry using the ␣ algorithm of Eq. (4); b) two-color pyrometry using the F algorithm of Eq. (7); c) one-color MAE pyrometry at 830 nm using Eq. (9); d) one-color MAE pyrometry at 1300 nm, also using Eq. (9); and e) two-color MAE pyrometry using Eq. (11). An example of temperatures calculated by each of these five methods from the same data set is shown in Fig. 3. The model of Dalzell and Sarofim [13] was

Fig. 4. Comparison of soot temperatures in a premixed ethylene/air flame from three variations of two-color (830 and 1300 nm) pyrometry, using the same emission data for each, with temperatures from a thermocouple. Error bars on the triangles represent the range of possible results obtained from the F algorithm method using the dispersion models of [13–16]. Error bars on the diamonds represent the uncertainty in the ␣ algorithm method, as reported by di Stasio and Sarofim [12]. ␾ ⫽ 2.29, height ⫽ 14.5 mm. The data points are displaced slightly in equivalence ratio (␾ ⫽ ⫾0.007) for clarilty.

used to obtain the soot refractive indexes for the F algorithm. Temperatures from the three absorption/emission methods are in good agreement with each other, but are lower by about 25 and 70 K than the temperatures from the ␣ and F algorithms, respectively. A square wave was chosen for the modulation pattern mainly because it enables the simplest explanation of the concept. A sine wave could also have been used with lock-in detection, which would improve the signal-to-noise ratio of the transmission measurements. Figure 4 shows a comparison of temperatures obtained from three different two-color methods using the same emission data for each, plotted against equivalence ratio. The solid symbols are from the optical data, and the open symbols are from thermocouple measurements. Temperatures calculated with the F algorithm using the refractive index model of Dalzell and Sarofim [13] are represented by triangles. The error bars represent the range of results obtained when other models of refractive index are used, including those by Lee and Tien [14], Habib and Vervisch [15], and Chang and Charalampopoulos [16]. The uncertainty in both the real and imaginary parts of the refrac-

SOOT PYROMETRY BY USING MAE tive index for each model was assumed to be 10%, for lack of a better estimate; none of the three sources reported uncertainties in their models. As shown in Fig. 4, the total uncertainty in the temperature from the F algorithm is ⫹100 K, ⫺75 K. This approach to determining the range of uncertainties in dispersion models closely follows that of di Stasio and Massoli [12], who reported similar ranges. The temperatures in Fig. 4 from the ␣ algorithm, depicted as diamonds, were calculated by using ␣1 ⫽ ␣2 ⫽ 0.95. The error bars represent the uncertainty of ⫾50 K that resulted from the analysis of di Stasio and Massoli [12] for this wavelength range. Uncertainties in the two-color modulated absorption/emission method, depicted as squares in Fig. 4, depend on soot volume fraction because it directly affects the signal to noise ratio of the absorption measurements. Measured values of fv ranged from 7 ⫻ 10⫺8 at ␾ ⫽ 2.13 to 4.5 ⫻ 10⫺7 at ␾ ⫽ 2.36. The resulting uncertainties in emissivity ranged from 14% to 4%, respectively, whereas the uncertainties in emission intensities ranged from 3% to 0.6%, respectively. As shown in Fig. 4, uncertainties in temperature ranged from ⫾92 to ⫾20 K for ␾ ⫽ 2.13 to 2.36, respectively. Absorption-based soot volume fractions (fv) were calculated from the transmission data by using equation [5] with the refractive index model of Dalzell and Sarofim [13], and ⑀␭ ⫽ 1 ⫺ ␶␭, with ␶␭ being the measured transmission at wavelength ␭. The resulting fv depended on wavelength, being about 15% lower for 1300 nm than for 830 nm. Emission-based fv were calculated using Eq. (5) substituted into Eq. (9), using the two-color MAE temperature and the measured emission intensity at wavelength ␭. The same refractive indexes were used as in the absorption fv. The emission fv was dependent on wavelength, being ⬃18% lower for 1300 than for 830 nm. This discrepancy, which appears both in the absorption and emission fv, points to the wavelength dependence of the refractive index model being incorrect. Because a large number of studies [1– 6] have already used this model near 830 nm, this wavelength was used for comparing absorption and emission fv. Fig. 5 shows a comparison of soot volume fractions obtained from the absorption method and the

1677

Fig. 5. Comparison of soot volume fractions calculated from absorption data (broken lines) and emission data (solid line) from the same experimental run as in Fig. 4. The dispersion model of Dalzell and Sarofim [13] was used for all calculations. ␾ ⫽ 2.29, height ⫽ 14.5 mm.

emission method (two-color MAE temperatures). This comparison shows that the emission results are on the order of 10% lower than the absorption. The emission-based results can be seen to show greater fluctuations. In order to produce agreement in fv at both 830 and 1300 nm from the emission data, K1 was held fixed at 5.16, and the ratio of K1/K2 was adjusted to give the best agreement, resulting in a change in the ratio from 0.87 given by the model to 1.05. DISCUSSION As a check that the Rayleigh criterion, 2␲r/␭ ⬍ 0.3, was met, particle sizes were estimated by considering the work of Vandsburger et al. [30], in which soot particle growth was examined in an ethylene/air flame. Their measurements of particle size vs. residence time were used, along with an estimated residence time at our measurement location, to estimate the particle in the present experiments. A first order estimate of the residence time was obtained by tres ⫽ h/Vgas, where h is the height of the measurement location above the burner surface, 14.5 mm, and Vgas is the velocity of the hot gases after combustion, estimated to be 40 cm/s, based on the conservation of mass and utilizing the known reactant flow rate and known flame temperature. This results in an estimated residence time of 36 ms, which corresponds according to the data from [30] to particle diameters of around

1678 60 nm. Using the shortest wavelength of the present experiments, 830 nm, the size parameter, 2␲r/␭, is calculated to be 0.23, so that the Rayleigh criterion was likely met. The agreement between the temperatures obtained by the three MAE techniques in Fig. 3 is remarkably good, and lends support to the validity of each of these methods. The measured temperatures of 1580 K obtained by the MAE methods, 1602 K by the ␣ algorithm, and 1645 K by the F algorithm may be compared with 1610 K measured by the F algorithm by Choi et al. [5], and 1603 K measured by thermocouple by Harris and Weiner [31] for similar ethylene/air flames at ␾ ⫽ 2.3. The agreement between all three flames is good, especially considering that the flames were produced in different laboratories. In Fig. 3, the emission-based results (F and ␣ algorithms) and the two-color MAE results show larger oscillations in temperature than the one-color MAE results. This is apparently due to the high sensitivity of the ratio of intensities to temperature. Figure 4 shows that a significant improvement in accuracy of soot temperature measurements is obtained with the proposed two-color MAE technique at values of ␾ near 2.3. At ␾ ⫽ 2.36, an improvement in uncertainty from ⬎ ⫾50 to ⫾20 K is achieved. However, at lower soot concentrations the benefit disappears as the signal to noise ratio (S/N) of absorption decreases. In the present experiment, the lower limit of fv at which the new method provided a significant benefit was about 3.5 ⫻ 10⫺7, corresponding to ␾ ⫽ 2.3, with a 60-mm path length. With improvements in laser stability, the S/N may be improved to provide benefits at lower soot concentrations. The upper bound of fv for which the new method is an improvement was not determined, since the flame became unstable at richer mixtures. However, the analysis of di Stasio and Massoli [12] shows that at fvL ⫽ 0.411 ␮m, corresponding to fv ⫽ 6.9 ⫻ 10⫺6 for L ⫽ 60 mm, temperature uncertainties using the conventional two-color methods are greater than 30 K for wavelengths greater than 800 nm. With the MAE method, the uncertainty should be significantly less than 20 K at these higher fv, perhaps as little as 10 K. The closeness of the agreement (⬃10%) be-

T. P. JENKINS AND R. K. HANSON tween absorption and emission fv in Fig. 5 suggests that the flame was nearly homogeneous, with some small degree of inhomogeniety being responsible for the lower emission fv. The oscillations in Fig. 5 in the emission fv are likely indicative of inhomogeneities in the flame, because the lengths of regions of high temperature may fluctuate while the overall path length through the flame remains relatively constant. The emission-based method would be more sensitive to such oscillations. Some research teams have suggested using comparisons of fv obtained by two-color emission with that obtained by transmission to evaluate the homogeneity of a flame [5, 32]. In homogeneous flames, the two methods are expected to agree. The agreement to within roughly 10% in the magnitudes between the methods in Fig. 5 shows that the flame in the present experiment had at least reasonable homogeneity, with the oscillations indicating the presence of some minor instabilities. The proposed MAE methods for temperature are insensitive to effects of fuel type and temperature on the refractive index. Dalzell and Sarofim [13], Habib and Versisch [15], and Siddall and McGrath [33] suggested that the optical properties of soot may vary with fuel type. Insensitivity to the type of soot may make the proposed method ideally suited for application to advanced combustors, where the conditions may vary greatly from those in laboratory flames. The accuracy of the one-color MAE method depends upon absolute calibrations of radiant intensity, and therefore is not as easy to apply as the two-color MAE method that relies only on the ratio of radiant intensities at two wavelengths. While calibrating, our collection solid angle was different than while measuring in the flame, thus introducing a potential error in the one-color method that would not affect the two-color method. The agreement between the methods in Fig. 4 indicates that the correction applied to account for this difference in solid angle was accurate in the present case. However, in general the two-color MAE method is expected to be more robust than the one-color method.

SOOT PYROMETRY BY USING MAE

1679

CONCLUSIONS

10.

A new method for measuring soot temperatures in flames has been proposed and demonstrated involving combined measurements of laser absorption and flame emission. The method was demonstrated by using two diode lasers, at 829 and 1304 nm, modulated at 1 kHz to enable the combined measurements. A significant advantage of the proposed method is that temperature can be obtained without having to rely on assumptions for the soot optical properties, which can result in uncertainties as large as ⫾ 100 K. In addition, the optical properties of soot may change with fuel type or flame conditions, perhaps making conventional two-color pyrometry unsuited for general use when the soot type is unknown. Like conventional two-color pyrometry, the method is restricted to cases where the soot particles are small enough to be in the Rayleigh regime. The MAE method was shown to offer a reduction in uncertainty by about a factor of three for a test case involving a premixed flat flame burner for which the soot volume fraction was on the order of 10⫺7. MAE pyrometry shows promise for accurate soot temperature measurements in some practical systems in which fv is on the order of 10⫺7 or greater, such as in diesel engines.

11.

This research was supported by the Office of Naval Research as part of the MURI program on pulse detonation engines, with Gabriel Roy as the technical monitor. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Sivathanu, Y. R., and Gore, J. P., J. Heat Transfer 114:659 – 665 (1992). Sivathanu, Y. R., and Gore, J. P., Combust. Sci. Technol. 80:1–21 (1991). Sivathanu, J. P., Gore, J. P., and Dolinar, J., Combust. Sci. Technol. 76. 45– 66 (1991). Klassen, M., Sivathanu, Y. R., and Gore, J. P., Combust. Flame 90:34 – 44 (1992). Choi, M. Y., Hamins, A., Mulholland, G. W., and Kashiwagi, T., Combust. Flame 99:174 –186 (1994). Sivathanu, Y. R., and Faeth, G. M., Combust. Flame 81:150 –165 (1990). Xu, F., Lin, K.-C., and Faeth, G. M., Combust. Flame 115:195–209 (1998). Arcoumanis, C., Bae, C., Nagwaney, A., and Whitelaw, J. H., SAE Paper 950850, 1995. Quoc, H. X., Vignon, J.-M., and Brun, M., SAE Paper 910736, 1991.

12. 13. 14.

15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

30. 31. 32. 33.

34. 35.

Wahiduzzaman, S., Morel, T., Timar, J., and DeWitt, D. P., SAE Paper 870571, 1987. Dyer, T. M., and Flower, W. L., in Particulate Carbon: Formation During Combustion (D. C. Siegla and G. W. Smith, Eds.), Plenum Press, New York, 1981, pp. 363–389. di Stasio, S., and Massoli, P., Meas. Sci. Technol. 5:1453–1465 (1994). Dalzell, W. H., and Sarofim, A. F., J. Heat Transfer 91:100 –104 (1969). Lee, S. C., and Tien, C. L. Proceedings of the 18th International Symposium on Combustion, The Combustion Institute, Pittsburgh, PA, 1981, pp. 1159 –1166. Habib, Z. G., and Vervisch, P., Combust. Sci. Technol. 59:261–274 (1988). Chang, H., and Charalampopoulos, T. T., Proc. Royal Soc. London A 430:577–591 (1990). Hottel, H. C., and Broughton, F. P., Indust. Eng. Chem. 4:166 –175 (1932). Liebert, C. H., and Hibbard, R. R., NASA TN D-5647, 1970. Kerker, M., The Scattering of Light and Other Electromagnetic Radiation. Academic Press, New York, 1969. Siegel, R., and Howell, J. R., Thermal Radiation Heat Transfer, 3rd ed. Hemisphere, Washington, DC, 1992. Wang, Y., Yao, M., and Liao, Y., SPIE 2594:75– 80 (1996). Jenkins, T. P., and Hanson, R. K., AIAA Paper 2000-3588, 2000. Svet, D. Y., Thermal Radiation. Consultants Bureau, New York, 1965. Lamprecht, A., Eimer, W., and Kohse–Hoinghaus, K., Combust. Flame 118:140 –150 (1999). Xu, F., Sunderland, P. B., and Faeth, G. M., Combust. Flame 108:427– 493 (1997). Latyev, L. N., Chekhovskoi, V. Y., and Shestakiv, E. N., High Temp. High Pressures 4:679 – 686 (1972). Bradley, D., and Entwistle, A. G., Br. J. Appl. Phys. 12:708 –711 (1961). Schoenung, S. M., and Mitchell, R. E., Combust. Flame 35:207–211 (1979) Kaskan, W. E., Proceedings of the 6th International Symposium on Combustion, The Combustion Institute, Pittsburgh, 1956, pp. 134 –143. Vandsburger, U., Kennedy, I., and Glassman, I., Combust. Sci. Technol. 39:263–285 (1984). Harris, S. J., and Weiner, A. M., Combust. Sci. Technol. 31:156 –167 (1983). Sivathanu, Y. R., Gore, J. P., Janssen, J. M., and Senser, D. W., J. Heat Transfer 115:653– 658 (1993). Siddall, R. G., and McGrath, I. A. Proceedings of the 9th International Symposium on Combustion, The Combustion Institute, Pittsburgh, 1963, pp. 102–110. Matsui, Y., Kamimoto, T., and Matsuoka, S., SAE Paper 800970, 1980. Najjar, Y. S. H., and Goodger, E. M., J. Heat Transfer 105:82– 88 (1983).

Received 22 August 2000; revised 13 March 2001; accepted 18 May 2001