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chapter 5 turbulent diffusion flames - FedOA

chapter 5 turbulent diffusion flames - FedOA

The parameter Kpp (cm -1

The parameter Kpp (cm -1 sr -1 ) denotes a differential scattering coefficient and is defined as the energy scattered per unit time and per unit volume into a unit solid angle direction θ. Finally, τλ, is introduced to account for the attenuation of the scattering when it travels between the scattering volume and the detector. The mean scattering coefficient for a size distribution of particles is given by: K = pp 52 NC Where N (cm -3 ) is the particle number density and C pp (cm 2 sr-1) is the mean cross-section for all spheres in the scattering volume given by: C pp = ∞ ∫ r= 0 C pp pp P( r) dr Where C pp is the differential scattering cross-section for a single homogeneous spherical particle of radius r. In the Rayleigh size limit, particle diameters much smaller than the incident wavelength, the expression of C pp in the vertical polarization orientation is: C VV 4 π mi −1 = 4 ∑ 2 4λ m + 2 And the horizontal polarization orientation is given by: C = C HH i VV i 2 2 cos θ 2 d 6 i

Finally, by combining these equations the differential scattering for Rayleigh size polydisperse particles is expressed as: 4 2 π mi KVV = 4 ∑ 2 4λ i mi 53 ( λ) −1 ( λ) + 2 Under the assumption of monodisperse system of particles, the mean particle size may be determined by combining the measured scattering and extinction coefficients, obtaining the followed relation: K K ⎧ m ( λ) −1 ⎫ 2 N d 2 3 3 − λ Im⎨ 2 ⎬ N id i m ( ) 2 ext ⎩ λ + ∑ i = ⎭ = f λ 2 2 6 VV 2 m ( λ) −1 ∑ N id i π 2 i m ( λ) + 2 Where d63 is the average diameter of the particles. i 6 i [ m( λ) , ] 1 d 3 63

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