## Pf kf df

(species mole fractions and

Thus, PDF and time-averaged values of individual species can be calculated if the mean values of mixture fraction (f ) and mixture fraction variance (fa) are known.

In several closure models, the covariance of two initially unmixed streams is related to the variance of a non-reactive scalar (Dutta and Tarbell, 1989). Many investigators have attempted to use the concept of probability density function (PDF) to evaluate higher order correlation appearing in time-averaged reaction source terms. The difficulties associated with the chemical reaction terms are thus shifted to computing the PDF of an inert scalar. The presumed PDF methods discussed above, assume a form for the PDF rather than computing it. From a computational standpoint, presumed PDF methods are straightforward extensions of moment closure methods. These methods also have been extended for non-adiabatic flow processes. In non-adiabatic processes, the local thermo-chemical state is not only related to mixture fraction but also to enthalpy. It is then necessary to employ a joint probability density function for mixture fraction and enthalpy. The presumed PDF methods have been widely employed in simulations of non-premixed combustion systems, and are mainstays of the engineering simulations of reactive flow processes (computational aspects of PDF-based models are discussed in Chapter 7). However, when there is

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