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Show IFRF Doc. No. K 70/a/12 August 1989 - 5 - Mathematical Modelling of Pulverised Coal Flames In this equation, U1 is the mean velocity component in the Xl direction, ~t is the effective viscosity, and mJ is the mass fraction of specie j. SCJ is the Schmidt number for specie j. The convective and diffusion terms of Equation 4 determine the rate the specie j is supplied to each numerical cell. The importance of diffusive and convective mixing is dependent on the velocity and length scales. In industrial burners, the physical distances between oxidant and reactant are large. Consequently, the convective and diffusive mixing require more time, and these mixing processes determine flame properties. On the other hand, at smaller scales, the combustion processes will be limited by eddy mixing or even chemical reaction kinetics since the transport of fuel and oxidant are fast. The micro-mixing inside a fluid eddy, in which the numerical cell is located, is the final step in the mixing process. In the model the fast chemistry approach is adopted and hence, the rate of combustion is directly related to the rate of micro-mixing. A simple model, which relates micro-mixing to the time scale of the fluid eddy, is applied [9] : Ro x = p x A Elk x [ mf u, Sf xmo x ] (5) In this equation, Rox is the rate of oxygen consumption in a volume; Sf is the stoichiometric oxygen requirement to burn 1 kg of volatiles; and mfu, mox and mpr are the mass fractions of fuel, oxygen and products. The operator, [] takes the smallest of the terms in brackets. The term k/At has the dimension of time and is related to the characteristic life time of the fluid eddies. It is instructive to compare this time scale with both the Taylor time scale of turbulence and the mean eddy life time. These can be estimated as follows: Taylor time scale 4k/t Time scale of mean size eddies Cu·1~ kIt = 0.16 kIt When the Taylor scale is dominant, the constant "A" equals to 0.25, but if the mean eddy scale dominates, "A" equals to 6.0. Value of 4 is generally applied in computations of combusting flows. Recently a detailed sensitivity study of predictions of semi-industrial swirling coal flames to the value of "A" constant were carried out. The value was varied in the range 0.25 to 6.0. The predicted flow field, temperatures, main combustion products were relatively insensitive to "A" with the exception of the swirl induced reverse flow region. To obtain good flame predictions, including the reverse flow region, a value around 0.5-0.7 should be used. For a number of swirling flames, the generally applied value of 4 gave 0.1% oxygen level predictions in the reverse flow while |