Two-dimensional soot aggregate sizing by multi-angle light ... · Two-dimensional soot aggregate...

Paper # 070DI-0254 Topic: Diagnostics

8th U. S. National Combustion Meeting Organized by the Western States Section of the Combustion Institute

and hosted by the University of Utah May 19-22, 2013.

Two-dimensional soot aggregate sizing by multi-angle light

scattering

Bin Ma Marshall B. Long

Department of Mechanical Engineering & Materials Science, Yale University New Haven, Connecticut 06520–8284 USA

This paper demonstrates two-dimensional soot aggregate size measurement in sooting coflow laminar diffusion flames using multi-angle light scattering. The experiment employed a pulsed laser at 532 nm that was focused into a sheet 7 mm high. The scattered light was imaged onto a cooled EMCCD camera with optics set to maximize spatial resolution while maintaining sufficient depth of field. The detection angle was varied from 10 to 90 degrees with respect to the laser beam. The distance between the camera and flame was kept constant to ensure the same collection efficiency. The Guinier analysis involves taking signal ratios of a near-zero angle to other angles. In order to obtain information in two dimensions, the images at different angles were geometrically warped to ensure spatial coincidence. The spatially transformed images at all angles were then correctly re-sampled. A set of eight ratio images was obtained and Guinier analysis was applied for each set of corresponding pixels. The normalized ratios at the eight angles were found to have good linear relations with respect to the square of the wave vectors, q, at these angles. The radius of gyration was then determined on a pixel-by-pixel basis from the slope of the ratio vs. q2 plot. A full two-dimensional map of soot radius of gyration was obtained by sequential measurements at different flame heights. Measurements were performed on C2H4/N2 coflow laminar diffusion flames at different dilution levels and, hence, soot loadings.

1. Introduction Soot is one kind of fine particulate matter under 2.5 µm (PM2.5) produced from incomplete combustion of hydrocarbon fuels, and is considered as an airborne contaminant with known adverse effect on human health. Strict regulations enacted on the emission of PM2.5 by air-quality agencies require tight control of soot formation, which in turn requires understanding of the formation mechanisms. In the soot formation process, nearly spherical primary particles are first formed from large polycyclic aromatic hydrocarbon molecules, and then agglomerate into larger fractal aggregates that may contain up to hundreds of primary particles. Various diagnostic approaches have been developed to characterize soot particles including sampling and optical techniques. Among the optical techniques, elastic light scattering (ELS) is a powerful tool to characterize soot aggregate properties. In particular, the soot aggregate size can be measured by a multi-angle scattering experiment performed in the so-called Guinier regime through a Guinier analysis. Gangopadhyay et


al. [1] applied the approach in measurement of soot aggregate size in a CH4/O2 premixed flame at several downstream points. The soot aggregate size was found to increase with height above the burner. Sorensen [2] provided an excellent review on the subject of light scattering by fractal aggregates, in which the multi-angle scattering technique was discussed in detail. Oltmann et al. [3] designed an ellipsoidal mirror to collect the scattering signals from one point in a wide range of angles; this allows the determination of soot radius of gyration through single-shot acquisition of the full scattering diagram. The approach was then applied in both laminar and turbulent flames, and very good agreement was reported when comparing to TEM measurements [4]. Most of the previous measurements, however, have been restricted to point measurements, where the radius of gyration was reported as a function of height above the burner (HAB). Two-dimensional full-field measurements are desired to understand better the soot formation process. In this work, the possibility of extending the Guinier analysis to two-dimensions through proper image processing is demonstrated. Two-dimensional maps of the effective radius of gyration are reported for two C2H4/N2 laminar diffusion flames. 2. Guinier Analysis Excellent theoretical reviews on light scattering by fractal aggregates are available in Refs [2,5] and only a brief introduction is presented here. An essential equation to describe soot aggregates is expressed as Eq. (1).

N = kRga

!

"#

$

%&

D

Eq. (1)

N is the number of primary particles in an aggregate; a is the diameter of the primary particle; Rg is the radius of gyration and is defined as the root mean square of the distances between each primary particle and the center of mass of the aggregate; D is the fractal dimension normally in the range of 1.7 to 1.8 for soot; and k is a proportionality constant of order unity. The radius of gyration is a representative parameter for aggregate size. The objective of aggregate sizing is to measure the parameter Rg. In the scattering experiment, an important experimental parameter is the wave vector !q defined as the difference of the incident and the scattered wave vector, and its magnitude is shown in Eq. (2).

q = 4!"!1 sin# / 2 Eq. (2) The wave vector !q is an experimental parameter and its magnitude can be set by choosing laser wavelength λ and detection angle θ. The inverse of q represents the probe length scale of the scattering experiment. The scattered light intensity from a collection of aggregates can be expressed as follows:

Isca q( ) = IincnNp2 d! p

d!S qRg( ) Eq. (3)


where Iinc is the incident laser intensity, n is the number of aggregates in the sample volume, Np is the

number of primary particles in a soot aggregate, d!p

d!is the scattering cross section of a primary

particle, and S(qRg) is the structure factor. Eq. (3) is valid under the assumption that negligible multiple scattering occurs and each primary particle scatters independently.

From Eq. (3) it can be seen that the ratio of the scattered signal Isca(0) at θ=0 and Isca(q) at a certain angle is a function of only the structure factor since other parameters in Eq. (3) are isotropic at any angle and cancel out. Furthermore, when the aggregate size is smaller or close to the probe length scale of the scattering experiment in the so-called Guinier regime (i.e., qRg ≤ 1) the ratio can be approximately expressed by Eq. (4), which forms the basis of the Guinier analysis.

Isca 0( ) / Isca q( ) = S 0( ) / S qRg( ) !1+ 13q2Rg

2, qRg "1 Eq. (4)

A routine procedure is to first obtain the ratios through a multi-angle scattering experiment, and then plot the ratios as a function of q2; the radius of gyration Rg can then be obtained from a linear curve

fitting with the slope to be 13Rg2 . The range of Isca(0)/ Isca(q) with good linearity is normally extended

up to a value of 2 [2,3]. Therefore the Guinier evaluation range of this study is also bounded by Isca(0)/ Isca(q) < 2. 3. Experimental Setup The experimental setup for multi-angle scattering is shown in Fig. 1. Two stable sooty coflow laminar diffusion flames with different fuel mixtures were investigated in this study. The fuels were 60% and 80% C2H4 by volume diluted by N2. The burner consists of a 0.4 cm inner diameter vertical tube, surrounded by a 7.4 cm coflow. The fuel velocity at the burner surface had a parabolic profile and the air coflow was plug flow, both with an average velocity of 35 cm/s. The burner was mounted on a programmable translational stepping motor for vertical movement. A frequency-doubled 532 nm Nd:YAG laser (Continuum PL-8010) with a repetition rate of 10 Hz provided the illumination. A 300 mm focal length cylindrical lens focused the laser to a vertical sheet that traversed the center of the flame. This gives a calculated sheet width of 5 µm, based on Gaussian beam assumptions. The long focal length lens is preferred to provide a near-constant beam waist across the flame. The laser beam was spatially cropped by an aperture to ~ 7 mm in height; only the central 2 mm region, where the intensity is more evenly distributed, was used for signal evaluation. Nevertheless, since the laser intensity Iinc term in Eq. (3) will be canceled out in taking ratios among warped images on a pixel-to-pixel basis, the laser beam profile (Gaussian or top-hat) does not seem to be critical to data quality, as long as they have a fixed distribution over the measurement time. A neutral density filter was placed in the optical path to attenuate the laser beam to an energy level of ~ 5 mJ per pulse to prevent laser-induced incandescence (LII). Negligible LII signal was verified by comparing the signals at 431 nm (collected through a narrowband interference filter) with the laser turned on and off. A pyroelectric power meter (LaserProbe RjP-734) was used to monitor the laser energy and to stop the beam. The measured laser energy was used for signal normalization to account for laser power fluctuations and drift. The multi-angle scattering experiment involves


imaging the soot-scattered signal at a set of angles. The detector was a cooled interline EMCCD camera (Andor Luca S) that was attached to a bar that rotated concentrically about the burner. The distance between the camera and the burner was fixed to ensure the same collection efficiency at each angle and each image was centered on the burner. The detection angle between the lens optical axis and the laser beam was varied from 10° to 90°. A 50 mm focal length camera lens with extension tube was coupled to the detector. The spatial resolution can be increased by using a longer focal length lens or using longer extension tubes for close-up imaging, however an increase in spatial resolution will result in a decrease in depth of field. The length projected onto a single pixel was 25 µm at a 90° detection angle, which corresponds to 144 µm at a 10° detection angle. A sufficient depth of field was maintained with the f-number set at 16. Each image averaged over 50 laser shots with the shortest available gate time of 470 µs. Good signal to noise ratio can be achieved within one shot given the strong soot-scattered signal, however 50 frames were integrated mainly for averaging small spatial variations of the flame caused by room air currents. For the sooty flames investigated in the study, the scattering signal is significantly greater (~ 2 orders of magnitudes greater in the sooty region) than flame luminosity. Nevertheless, flame background images were also acquired in the same way with the laser turned off and subtracted from the scattering signal images.

Fig. 1. Multi-angle elastic laser scattering setup 4. Image Processing The entire flame has been sequentially imaged from upstream to downstream, however only images at one downstream location are shown in this section to illustrate the image processing procedure. Raw scattering images taken at different angles from 10° - 90° are shown in Fig. 2. The image at the right-bottom corner is a normally observed image viewed at a 90° detection angle. When the camera was rotated around the burner to a smaller detection angle, the observed images became narrower in shape and the signal on each pixel was increased due to an increased sample volume as illustrated in Fig. 3. The laser beam waist has a finite width. The sample volume illuminated by the laser beam and then projected onto a pixel is shown as a red shaded area and is varied with detection angles. At angle θ, the sample volume V(θ) is a factor of 1/sin(θ) greater than the sample volume V(90) at an angle of 90°. The soot distribution is assumed to be uniform over the small sample volume and

Laser 532nm

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CD

ca

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!

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PM


therefore the signal is expected to increase by a factor of 1/sin(θ) from the 90° detection angle to a smaller detection angle θ.

Fig. 2. Raw scattering images taken at 10° - 90° detection angles as specified. The signal values are expressed by CCD counts.

Fig. 3. An illustration of the increased sample volume at a decreased detection angle. To perform the Guinier analysis in two-dimensions, the raw images must be first transformed to images with good spatial coincidence so that ratio can be directly taken on a pixel-to-pixel basis. The spatially transformed images must then be re-sampled to carry the correct intensity information (i.e. pixel value). In this study, the image transformation was performed through bilinear image warping in Matlab [6]. An image warping involves a geometric mapping from the coordinate space of a source image to that of a destination image, and a re-sampling procedure to determine the destination signals through an interpolation based on source signals. Bilinear image warping is an eight parameter warping that can be used to transform an arbitrary quadrilateral in the source image to an arbitrary quadrilateral in the destination image. The source coordinate (x,y) is correlated with the destination coordinate (u,v) through Eq. (5) [7].

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u = a10x + a01y+ a11xy+ a00v = b10x + b01y+ b11xy+ b00

Eq. (5)

aij and bij are the eight parameters that can be solved given an initial source/destination image pair. A target consisting of an equally spaced grid was fixed in the same plane as the laser sheet. Target shots were taken at a set of detection angles as shown in Fig. 4a. The 90° shot was chosen as the destination image while others are the source images. The same four non-collinear points on the target shots were chosen in each image. For every pair of source/destination images (e.g. 10°/90° or 70°/90°), four points (eight coordinate values) were used to solve for the eight parameters using Eq. (5). After the parameters were solved, the target shots in the source coordinates were spatially transformed into new images in destination coordinates as shown in Fig. 4b. Re-sampling of the images was performed by a bilinear interpolation. Good spatial coincidence was achieved in the transformed images. The images at smaller detection angle (e.g. at 10°) are shown to be blurrier mainly due to their smaller spatial resolution in the original image, which is a factor of ~ 5.8 [sin(90°)/sin(10°)] smaller than the resolution at the 90° detection angle.

Fig. 4a. The original target image viewed at a set of angles

Fig. 4b. The transformed target images

The same spatial transformation and signal interpolation procedure were then applied to the background-subtracted scattering images. The images were then normalized by a factor of 1/sin(θ) at


each detection angle θ due to sample volume considerations shown in Fig. 3. The warped scattering images were cropped and are shown in Fig. 5. The whole purpose of image warping in this study is to transform images taken at different angles to spatially coincident images, as a preparation for taking ratios on a pixel-to-pixel basis for the Guinier analysis in two-dimensions. During the image processing, it is important to make sure that the final warped images still carry the correct pixel signals. A useful check is to compare the total signal value of the original image and the warped image, as this total value should not be significantly altered by various image processing steps. The total signal was calculated by summing up all the pixel values in the frame, with any pixels outside the scattering region set to zero. The ratio of the total signal of raw images and warped images are calculated to be close to unity and are shown in Fig. 6.

Fig. 5. Warped scattering images at 10°-90° detection angles.

Fig. 6. The ratio of total signal of original images over warped images at various detection angles.

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Following the procedure of Guinier analysis, ratios of the I(0) image over I(θ) images were then taken. Since it is not possible to obtain the scattered signal at strictly 0°, 10° is often used as the smallest angle for taking ratios [2,4]. The ratio images are shown in Fig. 7 under the same scale. Average values were calculated for a small region in each of the ratio images and are shown as a function of q2 in Fig. 8. The position of the small region is illustrated by a red rectangle shown in the last image in Fig. 7. Good linearity is obtained in the Guinier evaluation range where Isca(0)/ Isca(q) < 2. A linear curve fitting was performed in the range and a R2 value of 0.9916 was obtained as a representation for the goodness of fitting. Rg was determined to be 138.8 nm from the slope of the fitted curve.

Fig. 7. Ratio images of I(10)/I(θ).

Fig. 8. The measured ratio of I(10)/I(θ) plotted as a function of q2 (Red dots) and a linearly fitted

curve (Blue line).

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5. Results and Discussion The same procedure was applied for the entire image, and sequential measurements at different heights at a step of 2 mm were composited together to yield a two-dimensional map of soot radius of gyration. The resulting soot aggregate sizes for the 60% and 80% C2H4 flames are shown in Fig. 9. The map of R2 values is also shown side by side to illustrate the quality of the linear fit. The maximum effective soot radius of gyration for the 60% and 80% flame are ~ 160 nm at ~ 45 mm HAB and ~ 200 nm at ~ 70 mm HAB respectively. The R2 for both flames are generally greater than 0.9. Since ratios of I(10°)/I(θ) were taken, the spatial resolution of the measurements is no better than 144 µm as limited by the resolution at 10°. The radius of gyration can be seen to increase with HAB. Since measurements were done sequentially for different HAB and detection angles, the data quality is affected by the effectiveness of the image warping procedure, i.e., how well the spatial matching can be achieved, as well as by the stability of the flame over time. As can be seen in regions close to the burner, strips were produced close to the edges, which are mainly due to the spatial mismatch of the warped images. This effect can be seen from Fig. 5, where two small peaks can be identified at radius of ± ~ 2 mm in the warped images with detection angle greater or equal to 30°, however the two small peaks can not be resolved in the 10° and 20° detection angles due to their smaller spatial resolution. Strips will be produced when taking ratios of a smeared image at 10° and a sharper image at larger angles. At the tip of the flame, the measured Rg also exhibits unrealistic values due mainly to the spatial flickering at the tip of the flame. In general, the 2D map of goodness of fitting parameter R2 can be used to indicate the confidence on the Rg results at each location.


Fig. 9. The radius of gyration (nm) and goodness of fit determined in two-dimensions for the 60%

(left) and 80% (right) C2H4 flames. Acknowledgements The research was supported by the DOE Office of Basic Energy Sciences (Dr. Wade Sisk, contract monitor) and NASA (Dr. Dennis Stocker, contract monitor) under contracts DE-FG02-88ER13966 and NNC04AA03A, respectively. References [1] S. Gangopadhyay, I. Elminyawi, C. M. Sorensen, Appl. Opt. 30 (1991) 4859-4864. [2] C. M. Sorensen, Aerosol Science and Technology 35 (2001) 648-687. [3] H. Oltmann, J. Reimann, S. Will, Combustion and Flame 157 (2010) 516-522. [4] H. Oltmann, J. Reimann, S. Will, Applied Physics B 106 (2012) 171-183. [5] A. Jones, in: Light Scattering Reviews, A. Kokhanovsky, (Ed.) Springer Berlin Heidelberg:

2006; pp 393-444. [6] MATLAB, R2012b; The MathWorks Inc.: Natick, Massachusetts, 2012. [7] C. A. Glasbey, K. V. Mardia, Journal of Applied Statistics 25 (1998) 155-171.

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Two-dimensional soot aggregate sizing by multi-angle light ... · Two-dimensional soot aggregate...

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