An Improved Turbulent Mixing Model

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Abstract
In application to turbulent reactive flows, both stochastic models and pdf methods require a model of turbulent mixing. Models currently in use are due to Curl (1963), Dopazo (1979), and Janicka, Kolbe, and Kollmann (1979). For the simple case of decaying fluctuations of a passive scalar in homogeneous turbulence, measurements suggest that the probability density function (pdf) tends to a Gaussian. All the moments of the standardized Gaussian pdf are finite and, in particular, the fourth moment (the flatness factor) is equal to 3. It is shown that the existing models produce pdf's that differ significantly from the Gaussian; in particular, the predicted flatness factors are infinite. An improved class of mixing models is presented that produces pdf's with finite standardized moments. The shape of the pdf produced depends upon the choice of two model parameters. These parameters can be chosen so that the flatness is as small as 3.12 (cf. 3 for a Gaussian), while the recommended model, which has a better overall performance, results in a flatness of 3.70. The shape of this pdf (shown on Figure 5) is close to Gaussian.