The use of the Lambert – Beer law allows to easily and directly perform particles volume fraction measurements (soot and NOC) in a uniform flow field (Fig. 2.8 (a)), i.e. fV constant in all the finite pathlength l, for example in laminar premixed flames [20 – 22, 26]. Different is the case of 2-D flow fields, for example, in axisymmetric laminar and turbulentdiffusionflames (Fig. 2.8 (b)). Tomographic techniques are therefore needed for reconstruction of the two-dimensional quantity under investigation. In particular, an Abel inversion can be used to reconstruct a cylindrically symmetric distribution from line-of-sight intensity measurements, Fig. 2.8 (b). This deconvolution is valid only when the measured signal is collected along infinitely thin, perfectly parallel rays [67, 68]. For these flame configurations, single-point measurements, i.e. LII and LIF, are more suitable than the absorption one. Volume fraction I 0 l l I Kabs Wavelength I −K abs λ = e I 0 50 ( )l Abel procedure I I 0 Volume fraction Radius Radius (a) (b) Fig. 2.8 Absorption measurements configuration for a uniform flow field (a), and in a 2-D flow field (b). 2.3.4 ELASTIC LIGHT SCATTERING Laser light scattering coupled with extinction measurements have been extensively used in combustion environments as tool for particle characterization.
With reference to the Fig. 2.9, when the beam of the laser passes through a cloud of spherical particles, the oscillating electric field, which is perpendicular to the direction of propagation of the wave, causes the electric charges of the particles to be set into forced oscillations with a frequency equal to the frequency of the incident light. These oscillating electric charges constitute sources of electromagnetic radiation, and hence generate what is termed scattered light . The measured scattered light Spp is related to the properties of the particles and the parameters of the optical system by the expression : S = I ΔΩΔVK pp pp 51 pp ηoptτ λ where Ipp is the incident energy flux, ΔΩ the solid angle aperture of the collection optics, ΔV is the scattering volume and ηopt accounts for the efficiency of the optical and electronic components comprising the detection system. The subscript p denotes the polarization stat (vertical or horizontal, see fig. 2.9), the first for the incident beam and the second for the scattered beam. Light Source x z I 0 H-pol y V-pol Extinction Volume ∆θ H-pol Scattering Volume θ Scattering Detector V-pol Extinction Detector Fig. 2.9 Light scattering and extinction experimental set-up. Adapted from D’Alessio A. .