Pressure correlations in turbulent reacting flows

Correlations with pressure represent a major difficulty in closing moment of pdf equations in reacting and nonreacting turbulent flows. The pressure satisfies instantaneously a Poisson-type equation for constant density flows, which leads to integrals over two-point correlations. For variable density flows, the pressure satisfies a hyperbolic equation describing acoustic wave propagation and hydrodynamic pressure variation. The effect of the fluctuations of density on pressure and its correlations with other variables are investigated. Density in combusting flows can be considered a bounded variable and then is the maximal fluctuation given by a jump process in time and space. This limit case of a pure jump process is taken as approximation for large density fluctuations. For diffusion flames, a further decomposition into mixing and reacting contributions can be obtained. The mixing contribution is negligible whereas the reactive part can be represented for certain correlations of the pressure as integral over the reaction surface S = O. A formal solution for the correlation of the pressure gradient with another fluctuation can be obtained as Neumann series. For the general case, however, only a representation of the pressure correlations as a sum of velocity, mixing, reacting, boundary parts could be established.