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Show dp f d . -z , d (u, df) ot dx, ox\a, ox,) dp^-+ (pu,f-') = - dt dx, d x. M, df-' a, dXl + G/i, ___ 3* (9) -cdp-f-k where the constants ot, Cg, C d take the values 0.7, 2.86, and 2.0, respectively. The mixture fraction variance is used in the closure model describing the turbulence-chemistry interactions (Fluent Users Manual, 1999). 2.2 SOOT MODEL In combustion processes, soot usually forms at the temperatures from 1000°C to 2500°C. The total amount of soot formed is always very small compared to the amount of carbon present in the fuel consumed. Its formation at high temperatures is usually accompanied or preceded by the formation of unsaturated hydrocarbons, especially acetylene and condensed unsaturated ring systems like polycyclic aromatics. These hydrocarbons are relatively stable thermodynamically, with respect to decomposition to the elements, and also kinetically stable as compared to paraffins or even olefins. Even in the presence of solid carbon, a certain amount of these hydrocarbons will remain in the gas phase in thermal equilibrium. The time available for soot formation is of the order of milliseconds. During this time, a solid phase of soot particles is formed from the fuel molecules via their oxidation and/or pyrolysis of products which generally involves: Nucleation: Fuel is decomposed and the first soot nuclei appears Coagulation: The soot particles collide and coalesce thereby forming the soot clusters Surface growth: Mechanism by which the bulk of soot mass is generated Oxidation: Soot is oxidized mamly by oxygen and O H to form gaseous products like C O and C 0 2. There are a few empirical models for the prediction of soot formation in combustion systems: the two-step Tesner model and the single step kinetic rate formulations are the most widely used soot models. In two step Tesner model, following (transport) equations for two scalar quantities, the radical nuclei concentration and the soot concentration are solved [Tesner et al, 1971]: dpn +dpUin _ d dt dx, x, '_______' + Rn (10) dpCs .dputcs _ 9 (flics' dt + Xi Xi + Rs K<Js °XiJ where n, Rn, cs, and R s are the radial nuclei concentration, the net rate of nuclei generation, soot concentration, and the net rate of soot generation, respectively; on and as are the turbulent Prandtl numbers for nuclei and soot transport. The net rate of soot generation in Tesner model is |
