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chapter 5 turbulent diffusion flames - FedOA

chapter 5 turbulent diffusion flames - FedOA

combustion systems:

combustion systems: laminar premixed flames, laminar and turbulent diffusion flames and practical systems like in engines. Furthermore, these efforts toward the understanding of the LII technique have been focused on the modeling and theoretically interpretation of the LII signal and on the improvement of the experimental procedures. On the basis of all the models, developed to describe the heating and cooling mechanisms important for LII detection of soot, there are same simplifications that can be so reassumed [54]: • As described above soot is mainly composed by spherical particles, called primary particles, with typical diameter in the range 10 – 30 nm, that agglomerate forming structure composed by a few up to thousands primary particles, Dobbins [28]. Normally, in the LII models these aggregates are idealized as composed by particles all of identical diameter, dp, touching at only one point. Therefore the soot volume fraction is simply given by the expression: fv = (π/6) N np dp 3 , where N is the number density of aggregates and np is the average number of primary particles per aggregate. • The second simplification assumes that the LII signal is based on the energy and mass balance between a single soot particle and its surrounding rather than the aggregate. • The third simplification requires that temperature gradients inside the particles can be neglected. Starting from the fundamental modelling work of Melton [53] the energy balance for a spherical particle of radius a can so write: 2 ( T − T )( π ) 38 2 4 4 4 dT ( 4πa ) εσ ( T − T ) − πa ρ c = 0 2 K a 0 4 a ΔH v dm 3 K abs ( a) π a q − + − SB 0 s s a( 1+ GK n ) M dt 3 dt

where the five terms represent in the order: the absorption rate of laser energy, the heat transfer by conduction, the vaporization energy of soot, the energy loss by blackbody radiation and the change in internal energy. However, for the correct interpretation of the incandescence signals, the different terms of the equation needs to carefully modeled. The absorption coefficient Kabs of soot strongly depends on: the absorption wavelength, λ, on the particle diameter, di, and on the complex index of refraction of soot, m = n+ik. In the Rayleigh regime (π di / λ

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