SESSION 8
OPTICAL AND RADIATIVE PROPERTIES OF SOOT PARTICLES
STRUCTURE AND BONDING OF CARBON CLUSTERS AND PARTICLES
PRODUCED DURING COMBUSTION
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" C_{60}, have been detected
as major percentage components in soot formed by high temperature combustion.
On the other side diamondlike films or particles can be easily produced by
hydrocarbon plasma assisted pyrolysis or quenched. Bonding of carbon containing
structures may range from pure sp^{3} 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
RayleighLorenz 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.
PREDICTION OF RADIATIVE ABSORPTION OF SOOT AGGREGATES IN
THE RAYLEIGH LIMIT
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 largescale 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 fractallike configurations of
spheres. The configurations are generated using a pseudorandom 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
RayleighGansDebye) 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 2050 % greater than those predicted from spherical Rayleigh
models at typical combustion temperatures. Secondly, it is shown that the
Rayleighlimit absorption properties of fractal aggregates scale according to
the ratio of the primary sphere radius ap and the aggregate radius of gyration
R_{g}. This behavior allows the development of a relatively
simple formula that
predicts Rayleighlimit 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
x_{C}=x_{V}(a_{p}/R_{g})^{1/4},
in which x_{V}=2a_{p}N_{S}^{1/3}/ is the
volumeequivalent size parameter of the aggregate. The curves of normalized
aggregate absorption efficiency vs. x_{C} 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.
THE RADIATIVE PROPERTIES OF SOOT AGGLOMERATES:
THE MODEL OF THE VIRTUAL REFRACTIVE INDEX AND FIRSTORDER MULTIPLE
SCATTERING
Rolf Dittmann
ABB Power Generation Ltd., Dept. KWGX, CH5401 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 flamegenerated
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. Firstorder
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 firstorder 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 socalled 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 firstorder multiple
scattering can be viewed to as a suitable tool in calculating the radiative
properties of soot agglomerates.
ON MEASURING THE MUELLER MATRIX ELEMENTS OF SOOT
AGGLOMERATES
R. Govindan, S. Manickavasagam and
M.P. Mengüç
Department of Mechanical Engineering
University of Kentucky, Lexington, KY 405060046, 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 fourelement Stokes vector. The interaction of an optical device with a
beam of light can be described as a transformation of an incident Stokes vector
[K_{i}] into an emerging Stokes vector [K_{o}].
[K_{o}]=[S].[K_{i}]
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 S_{11} and S_{12} elements are virtually identical to
their true values. These S_{ij} elements could be used in an inverse
algorithm to identify the size of soot monomers and agglomerates in flames.
^{1}Manickavasagam, S., Mengüç, M.P., (1995),
“Mueller matrix elements of fractallike soot agglomerates”Applied Optics
(submitted for publication).
