Original ArticlesDetermination of the Soot Volume Fraction in an Ethylene Diffusion Flame by Multiwavelength Analysis of Soot Radiation
Introduction
The understanding of soot production mechanisms and a knowledge of the soot distribution within combustion systems are key factors in several aspects of combustion. Combustion efficiency, heat transfer, and environmental pollution all depend upon soot production. Several efforts have been devoted to measuring the soot volume fraction, fv, in the harsh environment of combustion systems with the exploitation of existing techniques and the development of new ones. Due to their nonintrusiveness, optical techniques have received particular attention. The most established one is based on light extinction, frequently associated with scattering measurements for the simultaneous determination of soot particle size and number density 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. Refinements of the scattering theory have been recently developed to take into consideration the fractal nature of soot agglomerates 15, 16, 17, 18, 19, 20. Light extinction is a line of sight technique and gives integral values. In axial symmetric systems a mathematical procedure (Abel inversion) is used to achieve local values from a series of chordal measurements 21, 22, 23.
Recently, the technique of laser-induced incandescence (LII) of soot 24, 25, 26, 27, 28, 29, 30, 31 has received particular attention because of the possibility of obtaining spatially and temporally resolved measurements of soot in turbulent flames. Planar visualization of soot volume fraction distribution can be easily obtained, but for quantitative data a calibration procedure, mainly based upon extinction measurements or gravimetric sampling 27, 32, 33, is still necessary. Similar considerations apply to a recently developed technique based upon the detection of the laser-induced fluorescence of C2 molecules from laser vaporized soot (LIF C2 LVS) 34, 35, 36, 37.
A different approach based upon a two-color analysis of soot radiation has been widely used in practical situations, especially for studies in internal combustion engines 38, 39, 40, 41, 42, 43, 44. The simplicity of this technique is attractive under many of the severe constraints imposed in most practical systems. It readily allows the determination of averaged values of fv and temperature, which are the most significant parameters in engineering purposes. The reliability of the data depends on the calibration procedure and a knowledge of the index of refraction. A sensitivity analysis of the two-color emission technique [45] showed its critical dependence on the choice of the refractive index and a weak influence on the probability distribution of particle size.
Recently, the two-color and extinction techniques have been compared in a liquid pool flame [46] and in the homogeneous environment of a premixed ethylene/air flame [47]. The results obtained with the two techniques showed remarkable discrepancies, attributable to the presence of cold regions of soot and to the uncertainties in the refractive index determination. Furthermore, a comparison between soot volume fraction measurements obtained from the sampling and the extinction technique showed the latter to overestimate the soot volume fraction by a factor of about two [48]. The authors proposed the use of dimensionless absorption constant substantially higher than that usually adopted. These results would call into question most of the previous determinations of soot volume fraction reported in the literature. The present work uses a different methodology for the application of the emission technique and also performs extinction measurements on the same flame for comparison. Exploiting the axial symmetrical structure of our ethylene diffusion flame, we have calculated the local emission spectrum of soot through Abel inversion of each spectral component of the measured chordal spectra. With the data of Chang and Charalampopulos [49] for the index of refraction, local soot volume fractions measured from emissions compare well with those for extinction in the fairly large part of the flame where measurements were taken. A semiempirical approximation, of the form given by Siddal and McGrath [50], was also tested for the optical constants of soot, and the results are discussed.
Section snippets
Theoretical Background
The transmittance τλ of a monochromatic light beam through a homogeneous flame is given by the ratio of the emerging light intensity, IL, and the incident intensity, I0. It is related to the optical path length L and to the extinction coefficient Kext by the relationship The extinction coefficient can be expressed in terms of particle number density, N, and average cross sections for absorption, Cabs, and scattering, Csca: where ρsca is the
Apparatus and Procedure
An ethylene diffusion flame was produced on a coannular circular burner (10 mm i.d. and 100 mm o.d.), with a honeycomb inside the outer part of the burner to make the air flow as laminar as possible. The flame is shielded with a Plexiglas cylinder into which flat quartz windows are fitted; the laser beam reaches the probe volume through small holes in the shielding cylinder, facilitating the alignment procedure. The burner is fixed on an XZ motorized table (Daedal & Parker, Rohnert Park, CA),
Discussion
The flame was thoroughly explored (with steps of 0.3 and 5 mm in horizontal and vertical directions, respectively) by means of an extinction multiangular scattering technique. The method and the major results will be the subject of another paper. From these measurements, some selected radial profiles of the soot volume fraction are taken for comparison and are shown in Fig. 3. Considering the different set of refractive index used, the results are in good agreement with previously published
Conclusions
The presented multiwavelength emission method for the exploitation of soot luminosity to measure the local soot fraction appears to give quite satisfactory results. The Abel inversion applied to the chordal spectra and the utilization of a fairly large part of the emission spectrum are the most significant steps introduced here. The comparison with an independent optical technique gives satisfactory results, provided the same refractive index is assigned for both methods. However, the absolute
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