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Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applicationsClosed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.
Document ID
19920019576
Acquisition Source
Legacy CDMS
Document Type
Other
Authors
Madnia, C. K.
(State Univ. of New York Buffalo, NY, United States)
Frankel, S. H.
(State Univ. of New York Buffalo, NY, United States)
Givi, P.
(State Univ. of New York Buffalo, NY, United States)
Date Acquired
September 6, 2013
Publication Date
April 30, 1992
Publication Information
Publication: Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) for the Computational Analyses of High Speed Reacting Flows 37 p (SEE N92-28817 19-34)
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
92N28819
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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