Fractal Characteristics of Soot Particles in Ethylene/Air inverse diffusion Flame

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1 Advanced Materials Research Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Fractal Characteristics of Soot Particles in Ethylene/Air inverse diffusion Flame Jianyi Lu 1, a, Xin Cao 1,b and Chenglong Meng 1,c 1 School of Environmental Science and Engineering, North China Electric Power University, Baoding, , Hebei, P.R.China a lujianyi@tsinghua.org.cn, b caoxin0511@163.com, c @qq.com Keywords: Soot, fractal characteristics, inverse diffusion flame (IDF), respirable particles Abstract. Soot is produced in incomplete combustion of fuels, it is harmful to human health and the environment. Sampling points were set along the flame height of different air-fuel ratios in ethylene/air IDF and samples were tested by transmission electron microscopy (TEM). MATLAB software was used to process TEM images, calculated the fractal dimensions of soot samples and analyzed the fractal features. With the increasing of air-fuel ratio, the soot fractal dimension decreases, the size and the number of primary particles included in aggregates increase. With the increasing of flame height, the fractal dimension value decreases, and the size of primary particle increases, the aggregating soot particles are united loose. Introduction Soot is a by-product in any combustion process generated by human activities, it is the main source of respirable particles in the atmosphere. More than 90% of soot particles are less than 1µm, they are difficult to settle down, the residence time in the air is long, thus, soot has a great deal of harm to human health and the environment. B.B. Mandelbrot, the French-American mathematician, established fractal geometry when he was researching the coastline with self-similarity. The research objects of fractal geometry are systems which are self-similarity and disordered that exist in the social activity, and geometric figures which are irregular and not smooth in the nature and nonlinear systems [1]. Fractal dimension of soot particle along the exhaust pipe was between Mingrui Wei discussed the effects of temperature and pressure to fractal dimension of soot particles [2]. The fractal structure of particulate matter has impacts on characteristics of itself and other features, therefore, the study of fractal structure of atmospheric particulate matter has become an important issue. The fractal dimension is a description value for morphology of reunited soot particles, the larger the fractal dimension is, the more closely the basic soot particle reunites, otherwise the reunion is loose. In the form of fractal structure, the fractal dimension of particle surface describes its roughness. The larger the fractal dimension is, the rougher the particle surface is, and the stronger the adsorption ability of toxic substances is. Therefore, it is necessary to study fractal structure for the toxicity of particulate matter. Since the 1980s, foreign countries began to apply fractal theory to study the geometrical characteristics of atmospheric particulate matter. Wentazel identified the fractal dimension of diesel soot was 1.70±0.13, based on electron micrographs obtained by electron microscopy with high resolution [3]. Lee and Zhu got that: the fractal dimension was used to study soot generated during combustion process, and fractal dimension was used to describe the soot particles, exploring the surface reaction, sedimentation and the growth of soot particles. This paper provided an effective basis for measures to improve combustion efficiency and methods to reduce the environmental impact of soot. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Par, USA-12/05/16,15:10:14)

2 Advanced Materials Research Vols Study methods Experimental setup. The experimental setup is shown in Fig.1, samples were taen by this setup at flame height of 2mm, 7mm, 22mm, 27mm and 52mm respectively. The burner of inverse diffusion was composed of three concentric metal pipes, the inner was used to provide air, the fuel of ethylene was pumped in the middle pipe, and the outer was used to provide nitrogen to eep a steady flame. These three coaxial pipes were placed vertically and were fixed on the operating platform, their openings lied in the same horizontal plane. Between the concentric tubes, honeycomb metal strainer was filled to uniform airflow. The Teflon hydrophobic filter membrane with bore diameter of 0.22µm was installed in the sampler through the three-dimensional positioning platform. Starting at the bottom of the flame, sampling points were set in the bottom, middle and upper along the flame height. Soot samples were collected on filter membranes to be used for the detection of electron microscopy. We adjusted gas flow to control the air-fuel ratio at 0.6, 0.7 and 0.8 respectively, and maintain a stable flame height at 60mm. Fig.1. Experimental setup Transmission electron microscope (TEM). The principle of transmission electron microscope is using an electron beam shooting at the sample, its morphology and structure is determined through electron beams of transmission and reflection. The Tecnai G20, with high resolution, made by American FEI Company was used to detect samples, test conditions were room temperature and 200 V. Before testing, the membranes attached with soot samples were put in tubes, soaed in anhydrous ethanol, oscillated for fifteen minutes in ultrasonic instrument. Solution was draw with dropper, dropping a drop on the carbon film copper networ, after the sample was dry, tested it. In the testing process, samples were amplified to appropriate multiples, according to the need, then taing pictures. Box-counting dimension. In practical applications, fractal dimension referred to the box-counting dimension. By translating graphic image into digital image, we get a series of two-dimensional matrixes (binary images) shown by binary digits (0 and 1), then calculate the box-counting dimension of binary image. (1) The concrete steps of pixel-covering method to calculate box-counting dimension are [4] : 1) translating the gray image to binary image, mae each pixel point of image is only blac or white, obtain a data file, whose rans number is correspond with rans number of binary figure; 2) The date file is divided into lots, both numbers of rows and columns of each bloc are, and the number of N δ blocs with 0 or 1 are denoted as ( shorthand for N ), commonly, =1, 2, 4,, 2 i, that is, bloc is divided with pixel point of 1, 2, 4,, 2 i as side, the number of box is N 1, N 2, N 4,,N 2 i. Because the size of pixel point, δ, is the length of image divided by the number of pixel points in a row, the size of δ bloc with rows and columns composed of pixel points = δ (=1, 2, 4,, 2 i ). Due to δ is a δ constant to concrete image, the value of is substituted for in calculation. The date points logδ (, log N ), (=1, 2, 4 2 i ), are fitted by the least square in double logarithmic coordinate, the negative slope of the line is the physical box-counting dimension of image.

3 1198 Advanced Energy Technology (2) Decreasing sequence of pixel-covering method: there are many ways to construct a decreasing sequence, halving sequence is widely used, that is, successive mae a halving of image. The maximum value of used sequence depends on the image size, the minimum value of the grid is always 1, which is the limit of the mesh. By the definition of fractal dimension, the smaller the bloc size is, the more accurate calculation of the fractal dimension is. Fractal image stored in computer can only be divided to pixel size. Therefore, when discussing fractal nature of the image, we can tae the size of a pixel point as the lower limit. In the calculation process of fractal dimension, appropriate numbers of test points are needed to avoid the singular situation, the upper limit can be determined according to specific circumstances and requirements. Results and discussion TEM images. Figure 2 is two TEM photographs of typical soot particles with air-fuel ratio is 0.6, the flame height are 2mm and 27mm, respectively. Soot particles in the two heights formed significant differences in size and morphology. At the flame height of 2mm, soot particles are relatively very small, there are no more basic soot particles together to form soot. While the size of basic soot particles at flame height of 27mm is larger, they reunite to form massive reunion soot; these soot particles have not very clear edges, probably covered with volatile substances. Figure 3 is two TEM photographs of typical soot particles at the same flame height of 22mm, with two different conditions (air-fuel ratio is 0.6 and air-fuel ratio is 0.7). From the figures, we can see that soot particles are relatively very small with air-fuel ratio of 0.6, there are no more basic soot particles reunited to form soot. The size of basic soot particle with air-fuel ratio of 0.7 is larger, they reunite to form massive reunion soot. On the other hand, we can also observe that the number of elementary particles for reunion soot at smaller air-fuel ratio is less, thus the total number of soot particles is larger than the number of larger air-fuel ratio. Fig. 2-A. H=2mm, φ=0.6 Fig. 2-B. H=27mm, φ=0.6 Fig.3-A. φ=0.6 H=22mm, Fig.3-B. φ=0.7 H=22mm, Image binarization. The original image of fractal is generally gray (color image can be processed into a grayscale image), when we use box-counting dimension to calculate the fractal dimension of image, firstly, concerned area should be extracted from the image, then in dealing with the adjustment of gray-scale, feature detection, boundary recognition, and so on, converting the gray image to blac and white bitmap. We use programs to convert TEM image to binary image. Binary figure and binary histogram of TEM image with the woring condition of flame height at 27mm and air-fuel ratio of 0.7 are shown in Fig.4:

4 Advanced Materials Research Vols Fig.4-A. TEM figure Fig.4-B. Binary figure Fig.4-C. Binary histogram Fractal dimension and fractal characteristics. In this paper, fractal dimension of image obtained by transmission electron microscopy is calculated by MATLAB software, fractal dimensions of each woring condition are shown in the Table 1. Fractal dimension is largest in air-fuel ratio of 0.6, the fractal dimension decreases with the air-fuel ratio increases. This is because soot particles are small in little air-fuel ratio condition, chances of collision are less in the same environment. The reunion particles are close together when a small amount of soot particles collide, so that the fractal dimension is large. With the increasing of air-fuel ratio, the size of basic soot particles increases, a large-scale reunion soot particles form, the number of basic particles increases, the structure is loose, fractal dimension decreases [5]. Table 1 Fractal dimensions of different woring conditions and different flame heights flame height 2mm 7mm 22mm 27mm 52mm air-fuel ratio Conclusions By writing MATLAB programs, the box-counting dimension of image is calculated, and it is applied to structural characterization of soot particles, results showed that: 1) TEM photos show that different stages of soot particles present different appearance characteristics. MATLAB has powerful image processing and programming functions, it can process images easily, processed binary figure can be accurately calculated the fractal dimension by MATLAB. 2) Analysis of the fractal dimension at the same height with different air-fuel ratio, we found that: fractal dimension is larger with smaller air-fuel ratio; and fractal dimension is smaller with larger air-fuel ratio, which indicates that soot particles reunite more loosely with a large air-fuel ratio, the adsorption capacity of toxic substances is wea. 3) In the vicinity of 2mm, soot particles begin to reunite and coagulate, reunited particles are less, generated particles are more closely, and fractal dimension is bigger. In the vicinity of 27mm, a large number of reunion particles have formed, the formation mechanism between reunion soot particles is dominant, the structure of reunited particles is relatively loose and the fractal dimension decreases. Along with the agglutination reaction and the adsorption of soot particles on sediments, the structure becomes closely and the fractal dimension increases at the flame height of 52mm. 4) When the box-counting dimension of digital image is calculated by MATLAB, we should pay attention to the following three points: a) Select appropriate image resolution; b) Select appropriate upper regulation value or appropriate fractions; c) Mae full use of superior image processing functions of MATLAB.

5 1200 Advanced Energy Technology Acnowledgements This wor is supported by the National Natural Science Foundation of China (Grant No ) and the National Natural Science Foundation of Hebei Province (Grant No. E ). References [1] Qiwen Wang. Journal of Tongren Teachers College, 2006, 8(5):54-57 (In Chinese). [2] Mingrui Wei, Huiya Zhang, Liang Kong, Weidong Zhao. Progress in Natural Science, 2008, 18(9): (In Chinese). [3] Wentazel M, Gorzawsi H, Naumannc H, et a1. Aerosol Science, 2003, 34(10): [4] Feng e Wang, Jinliang Wang, Changxing Zhu. Journal of Liaocheng University (Nat. Sci.), 2008, 21(2): (In Chinese). [5] Zheng Li. Development of Premixed Combustion Analysis Systems and the Effects of Synthesis Conditions on the Soot Structure Properties [D]. Mechanical Institute of Tianjin University (In Chinese)

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