# A new multi-scale mixing model for turbulent reacting flows

Abstract (Summary)

In the probability density function (PDF) description of a turbulent reacting flow, the local
temperature and species concentration are replaced by a high-dimensional joint probability density
function that describes the distribution of states in the fluid. The PDF has the great advantage
of rendering the chemical reaction source terms closed, independent of their complexity. However,
molecular mixing, which involves two-point information, must be modeled. Indeed, the qualitative
shape of the PDF is sensitive to this modeling, hence the reliability of the model to predict even the
closed chemical source terms rests heavily on the mixing model. Spectral models contain two-point
statistical information of the velocity and scalar fields that can accurately capture all of the spectral
dynamics of the scalars (enthalpy and species mass fractions). A new closure called ‘multi-scale
mixing model’ is presented for the mixing terms based on a spectral representation of the scalar
field.
Such a closure is developed in two levels. In level A, the eddy damped quasi normal Markovian
(EDQNM) model, extended to multiple scalars by Ulitsky and Collins (2000), has been applied to
the study of mixing of differential diffusing scalars and completely validated by direct numerical
simulations (DNS). In level B, the ‘multi-scale model’ of mixing is then developed based on this
EDQNM closure. This model is implemented as an ensemble of stochastic particles, each carrying
scalar concentrations distributed across different wavenumbers. Scalar exchanges within a given
particle represent “transfer” while scalar exchanges between particles represent “mixing.” The
model correctly predicts the evolution of an initial double delta function PDF (unmixed condition)
into a self-similar Gaussian as seen in DNS by Eswaran and Pope (1988a). Comparisons of the
model with DNS are in good agreement and extensions to multiple scalar mixing are also presented.
To bring in the effect of chemical reactions, a new EDQNM model for a bimolecular reaction is
developed (level A). This model is validated with DNS for a bimolecular reaction for unmixed initial
conditions. A widely used PDF mixing model, Interaction by Exchange with Mean (Dopazo (1975))
model fails even to qualitatively capture the product-reactant correlations, an essential statistic for
multi-step chemical reactions, while EDQNM, due to the fact that it retains spectral information,
is able to do a better job at predicting this statistic. Work has been initiated to include the effect
of reaction into the multi-scale mixing model described earlier.
Bibliographical Information:

Advisor:

School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

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