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EXPERIMENTAL CORRELATION OF SOOT SPECTRAL ABSORPTION
COEFFICIENT
A relatively simple empirical relation for the absorption
coefficient kλ,
found experimentally in some instances, is
where C is the soot volume concentration (volume of
particles per unit volume of cloud), and k is a constant. The λ is
in μm for the numerical quantities given here. Hottel (1954) recommends
using
for λ > 0.8 μm. In some experiments, Siddall
and McGrath (1963) also found the functional relation of (D-4) to hold
approximately. They give, in the range λ = 1-7 μm, the following
mean values of α:
In Köylü and Faeth (1996) the extinction by soot was examined
for acetylene, propylene, ethylene, and propane. The exponent was found as α =
0.83 ± 0.08 for all of these fuels. This was reasonable for the spectral range λ
= 0.514–5.2 μm.
In Siddall and McGrath (1963) the data were inspected in more
detail to see whether α had a functional variation with λ that would provide a
more accurate correlation than using a constant α. In some instances α took the
form
where c1 and c2 are
positive constants. Examples are in Fig D-1. In other cases, a more general
polynomial was required to express α as a function of λ, Fig. D-2. Thus,
as a generalization of (D-4) for the infrared region,
and letting α be a constant is only an approximation.
FIGURE D-1
Experimental values of the exponent a plotted against l for
cases where a varies approximately linearly with ln l [Siddall and McGrath
(1963)].
FIGURE D-2
Experimental values of the exponent a plotted against l for cases where a does
not vary linearly with ln l [Siddall and McGrath (1963)].
In the visible range
experimental data led to the recommended form [Hottel (1954)]
for the wavelength region around λ = 0.6 μm (λ
≈ 0.3 – 0.8 μm). |
