Apr 6, 2007 - ... England and Wales Registered Number: 1072954 Registered office: Mortimer House, .... lations of Jones (1979a, 1979b) and Borghese et al.
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Effective Diameter of Agglomerates for Radiative Extinction and Scattering a
Sunil Kumar & C. L. Tien
a
a
Department of Mechanical Engineering University of California , Berkeley CA 94720, USA Published online: 06 Apr 2007.
To cite this article: Sunil Kumar & C. L. Tien (1989) Effective Diameter of Agglomerates for Radiative Extinction and Scattering, Combustion Science and Technology, 66:4-6, 199-216, DOI: 10.1080/00102208908947150 To link to this article: http://dx.doi.org/10.1080/00102208908947150
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Combust. Sci. ami Tech.. 1989. Vol. 66, pp. 199-216 Reprints available directly from the publisher Photocopying permiued by license only
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Effective Diameter of Agglomerates for Radiative Extinction and Scattering SUNI L KUMAR and C. L. TIEN Department of Mechanical Engineering University of California, Berkeley CA 94720. USA
Downloaded by [New York University] at 10:44 17 April 2015
(Received April 5, 1989; in final form July 24, 1989)
Abstract-This study examines the extinction and scattering characteristics of randomly oriented agglomerates consisting of closely-packed small identical spherical particles such as soot in flames. An equivalent sphere is introduced as one that exhibits similar scattering or extinction cross-section as the agglomerate and has the same refractive index as the primary particles. A simple analytical reasoning is presented that establishes the ratio of the diameter of this sphere to the diameter of the primary particles to be proportional to the cube root of the number of particles in the agglomerate. Simple expressions for the proportionality constants for various morphologies are developed. Previous studies in literature have used extensive numerical computations to empirically correlate the above proportionality without considering the proportionality constants. Scattering patterns for various morphologies are also predicted which have significance for optical diagnostic techniques. Keywords: Optical Diagnostics, Soot, Particles, Scattering, Extinction.
NOMENCLATURE
a, a', b
H(P)
elements of tensor T j l complex number in the definition of ( cross-section elements of tensor T]I diameter unit vector electric field vector fractal dimension solid volulme fraction, 4Nn(D/2)J /3V form factor to account for coherent addition of intensities radial distribution of number density Green's function in spherical geometry spherical Bessel functions 3(sin p - pcos p)/pJ
i
FT
A
C c, d, e D
e E
f J: F(O)
g(R)
G(r, r) h~m)
I
i; k K
m n N p p~m)
Q r
intensity, energy/steradian/projected area Bessel function propagation constant, 2n/). constant in the fractal densi ty distribution complex refractive index, n + i« index of refraction number of particles in agglomerate constant in the fractal density distribution Legendre function efficiency posi tion vector 199
200
R t
Til
V
x,y, z
X, y ()(
y I:
t /1
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