Abstract
The analysis of probability density function (pdf) equation is performed to understand the turbulent flame and flow properties with density variation effects. The calculation results, based on single concentration pdf equation, are presented with different assumptions concerning the small scale mixing for a premixed turbulent flame in unconfined space. The plume geometry and the burning rates fairly depend on the used assumptions for the thermal expansion and turbulent diffusivity. Therefore, the velocity-concentrations joint pdf equation solution is needed. For this equation the moment method based on semi-invariant formula for characteristic function (cf) is used. A series of approximations are proposed with restrictions on the order of the used moments. The peculiarities of the second order approximation are illustrated by the results of the plane turbulent jet calculations. The set of the moment equations presented for the self-similarity variables is degenerated and the conditions on the plane of symmetry permit to calculate the turbulent intensities on this plane and to build the solution for the free jet. Further progress in turbulent flame modeling is connected with developing the turbulence modeling which could be used for the usual turbulent flames geometry.
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