A. D'Alessio
Dipartimento di Ingegneria Chimica
Universitá "Federico II", Napoli, Italia

Carbon containing submicronic particles and clusters produced during combustion have relevance for the prediction of radiative heat transfer in combustion systems or at ambient temperature for the thermal balance of the atmosphere. The spectral dispersion of absorption and scattering coefficients of particles from the near u.v. down to the infrared is a necessary input for radiative heat transfer models. The spectroscopic and optical properties are direct expression of the structures and bonding of the particles and clusters, therefore a preliminary discussion of our knowledge on this matter is required. In the last few years great progress has been made in the physical and chemical characterization of carbon containing structures produced at high temperatures; fullerenes, including the "magic bucky ball" C60, have been detected as major percentage components in soot formed by high temperature combustion. On the other side diamond-like films or particles can be easily produced by hydrocarbon plasma assisted pyrolysis or quenched. Bonding of carbon containing structures may range from pure sp3 states passing through intermediate combination of both typed of bonding, with different degree of medium range spatial organization inside the particles . In addition, the long range organization of the structures, i.e. their typical size and shapes, is determined by the clustering, surface growth and coagulation/agglomeration processes, and exhibits a clear multimodal size/shape distribution functions. Spectroscopic and optical effects like absorption, fluorescence, Raman, and Rayleigh-Lorenz light scattering can "probe", according to the case, short, intermediate and long range organization of nuclei and electrons inside the structures. They also yield information on bonding, cristallinity, and overall size and shapes of carbon containing structures. Illustration of these examples will be discussed from recent spectroscopic work obtained by different groups operating with premixed flames, shock tubes and analogue experiments for interstellar dust research.


Daniel W. Mackowski
Department of Mechanical Engineering
Auburn University, AL, 36849, U.S.A.

It is well known that thermal emission from soot particles can constitute the dominant fraction radiative heat transfer from large-scale flames. Typically, the sizes of aggregated soot particles will be considerably smaller than the infrared radiation wavelengths associated with thermal emission in flames. Because of this, the radiative absorption properties of the soot aggregates - which are essential to accurately model radiative transfer in flames - can be predicted using an electrostatics (or Rayleigh limit) analysis. Such an analysis is presented here. In the electrostatics limit the radiative absorption and scattering properties of a particle can be obtained from solution of Laplace’s equation for the particle configuration. A general analytical solution of Laplace’s equation, based on a coupled spherical harmonics formulation, is developed for multiple sphere configurations that are characteristic of aggregated soot particles. The method enables the determination of the effective polarizability of the soot aggregate, from which the scattering and absorption cross sections of the aggregate can be obtained. Calculations of soot absorption are performed on fractal-like configurations of spheres. The configurations are generated using a pseudo-random algorithm which creates a sequence of sphere positions that exactly satisfy the fractal relationship for prespecified values of fractal dimension and prefactor constant. Results indicate that, first, the independent sphere (or Rayleigh-Gans-Debye) model, in which the aggregate absorption cross section is given as sum of the primary sphere cross sections, can significantly underpredict the absorption of the aggregate when the real and imaginary parts of the sphere refractive index are large. For refractive index values typical of carbonaceous soot in the IR wavelengths the aggregate absorption cross section can exceed the sum of the sphere cross sections by as much as 100 %. Because of the spectral variation of carbonaceous soot refractive index this effect is expected to be most significant in the near to mid IR radiation wavelengths, and can lead to Planck mean absorption coefficients that are on the order of 20-50 % greater than those predicted from spherical Rayleigh models at typical combustion temperatures. Secondly, it is shown that the Rayleigh-limit absorption properties of fractal aggregates scale according to the ratio of the primary sphere radius ap and the aggregate radius of gyration Rg. This behavior allows the development of a relatively simple formula that predicts Rayleigh-limit aggregate absorption efficiency for arbitrary fractal dimension and number of spheres in the aggregate. Finally, the behavior of aggregate absorption in the resonance region (i.e., comparable aggregate sizes and radiation wavelength), obtained via exact solution of Maxwell’s equations for the sphere configuration, is discussed. By normalizing the aggregate absorption efficiency with that obtained in the Rayleigh limit, it is shown that the absorption properties of aggregates having arbitrary size parameters, fractal dimension, and number of spheres can be represented by a single, characteristic size parameter xC=xV(ap/Rg)1/4, in which xV=2apNS1/3/ is the volume-equivalent size parameter of the aggregate. The curves of normalized aggregate absorption efficiency vs. xC are shown to be a function solely of primary particle refractive index. Implications of the results on the effects of soot on flame emission and radiative propagation in the atmosphere are discussed.


Rolf Dittmann
ABB Power Generation Ltd., Dept. KWGX, CH-5401 Baden, Switzerland

Investigations on the radiative heat transfer within densely particulate laden combustion systems require knowledge of the electromagnetic cross sections of the combustion aerosols. Commonly, calculations based on the Mie theory for isolated spherical particles of arbitrary size are applied. Assuming isolated spherical particles the Rayleigh approximation is also suitable in performing calculations within the far infrared region of the electromagnetic spectrum.

Numerous expermental investigations on the morphology of flame-generated aerosols, however, showed the presence of agglomerates formed by up to several hundred spherical primary particles arranged in fractal structures. Thus, the use of the Mie theory as well as the Rayleigh approximation is a priori rather questionable as the electromagnetic interaction within the agglomerate must be taken into account. Many efforts, therefore, have been made during the recent years in order to describe the optical cross sections of agglomerated soot particles.

Most of the methods published are limited to primary particles within the Rayleigh limit. Thus, uncertainities are inherent in utilizing these methods calculating the radiative transfer within high temperature flames with an important amount of thermal radiation in the near infrared or even visible wavelengths. The knowledge of the optical cross sections of real combustion aerosols is also important in optical aerosol characterization where the application of visible wavelength has to be preferred due to a minimization of disturbance caused by thermal radiation. Consequently, a method is required which provides the possibility to describe the electromagnetic interaction of nearby spherical particles of arbitrary size.

The electromagnetic interaction may be considered as multiple scattering within an agglomerate. Thus, in this presentation at first a qualitative analysis of the multiple scattering effects within an agglomerate is performed. First-order multiple scattering is found to provide a sufficient approximation to the particle interaction as, due to the strong absorption of the particles under consideration, the intensity of the scattered light decreases rapidly with increasing multiple scattering order. Furthermore, if large agglomerates of fractal structure are considered arbitrary phase shifts of the multiple scattered light in higher orders are found, thus leading to extinguishing scattered electric fields.

With knowledge of the first-order multiple scattering approximation the remaining task is to quantify the secondary scattering. The problem arising here is the anharmonic behavior of the scattered electromagnetic field in space within the near field zone. Thus, a major condition for the application of the Mie theory is not satisfied. In order to enable a solution, though, a transformation is found providing a formal description of the electromagnetic field scattered once as an electromagnetic oscillation harmonic in space and time. Subsequently, introducing the so-called virtual refractive index, the secondary scattering can be described by a modified Mie formulation. The virtual refractive index enables the calculation of the secondary scattering for spheres of arbitrary size even at the closest particle distance possible. Due to the simplicity of the model presented, it can be applied to agglomerate geometries as as real combustion aerosols with little numerical expense.

By means of this model a general formula for the light extinction caused by soot particles agglomerated in fractal structures was found. Results were compared with those available in literature for small primary particles within the Rayleigh limit as well as with results for the light scattered by a very special agglomerate geometry consisting of larger primary particles. In all cases an excellent agreement was found proving the validity of the model presented. Furthermore, extinction cross sections were calculated for agglomerates consisting of primary particles with the diameter up to the magnitude of the light wavelength. Although no reference data were available here, the results were throughout consistent.

Summarizing, the model of the virtual refractive index and first-order multiple scattering can be viewed to as a suitable tool in calculating the radiative properties of soot agglomerates.


R. Govindan, S. Manickavasagam and M.P. Mengüç
Department of Mechanical Engineering
University of Kentucky, Lexington, KY 40506-0046, U.S.A.

Understanding the formation of soot particles and agglomerates in flames is very important in order to design more efficient, economical and environmentally friendly combustion systems. The scattering characteristics of soot particles and agglomerates reveal more about their size and can be used to determine their volume fraction distribution in flames. In particular, the angular dependence of scattering of various states of polarized light from small particles and agglomerates can yield much information about the nature of the scatters. In this paper we make use of this concept to propose an experimental procedure which can be used to obtain accurate information about the physical properties of the soot agglomerates.

The intensity and polarization of a beam of light can be completely specified by the four-element Stokes vector. The interaction of an optical device with a beam of light can be described as a transformation of an incident Stokes vector [Ki] into an emerging Stokes vector [Ko].

where [S] is the 4x4 matrix known as the Mueller or scattering matrix. It is a characteristic of the optical device or the medium causing the transformation.

Recently, Manickavasagam and Mengüç (1995) discussed the variations of the Mueller matrix elements of different soot agglomerates and showed how these can be used to recover the agglomerate size, structure and volume fraction in flames. Here, we propose an optical setup as shown in Fig. 1 to measure the Mueller matrix elements for particles in flames.

This setup uses a laser along with several retarders (half and quarter wave plates) and polarizers. The orientation of the optical components with respect to the optical axis is varied several times and the scattered intensity distribution is recorded each time. This leads to a set of linear equations from which the Mueller matrix elements can be easily recovered. Even though this method uses subtractive techniques to obtain the six elements, the accuracy is not affected because the elements to be recovered appear as significant differences between large quantities.

Figure 1. Schematic of the Experimental Setup; POL: Polarizer, HWP: Half wave plate, QWP: Quarter wave plate, F: Flame

The second part of the paper presents the results of a sensitivity analysis performed to determine the optimum set of combinations of the optical components so that the desired Mueller matrix elements of soot agglomerates can be recovered accurately. For this, theoretical results for the matrix elements of soot agglomerates are taken from the AGGLOME algorithm.1 It is found that the most important parameter that affects the accuracy of the recovered matrix elements is the condition number (CN) of the coefficient matrix in the linear system of equations. If the CN is large, then the Mueller matrix elements determined from experiments would not be reliable. However, by using a proper combination of the optical components, one can reduce the CN to be less than 10. In this case, it is shown that even if there is 7.5 % error in measured intensities, the recovered S11 and S12 elements are virtually identical to their true values. These Sij elements could be used in an inverse algorithm to identify the size of soot monomers and agglomerates in flames.

1Manickavasagam, S., Mengüç, M.P., (1995), “Mueller matrix elements of fractal-like soot agglomerates”Applied Optics (submitted for publication).

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