Closure models for turbulent reacting flows

Abstract

In this paper, a simple procedure based on fast and slow reaction asymptotics has been employed to derive first-order closure models for the nonlinear reaction terms in turbulent mass balances from mechanistic models of turbulent mixing and reaction. The coalescence-redispersion (CRD) model, the interaction by exchange with the mean (IEM) model, the three-environment (3E) model, and the four-environment (4E) model have been used to develop closure equations. The closure models have been tested extensively against experimental data for both single and multiple reactions. The closures based on slow asymptotics for the CRD, 3E and 4E models provide very good predictions of all of the experimental data, while other models available either in the literature or derived here are not adequate. The simple new closure equations developed in this paper may be useful in modeling systems involving turbulent mixing and complex chemical reactions. showed that all of these models possess an analogy to theories of isotropic turbulent micromixing as expressed by AlChE Journal -_ cm'/s rnol/m' k , = 1.3 x 10' m'/mol/s; k2 = 2.3 m'/mol/s; 7" = 2.0 s; U = 1.6 cm/s AlChE Journal

DNS, LES and Stochastic Modeling of Turbulent Reacting Flows

“…The parameter -' can also be related to the ensembleby the models described above are compared with those obmean value of the reacting scalar. This relation is obtained by tained by employing the 3E model of Dutta and Tarbell (1989) substituting Eq. 3 into Eq.…”

“…In this prietsaitc fteratn il r eae otoeo wre u roc ts in the aprb ase d on an appropriate conserved scalar variable, hereby denoted by work, we use recent developments in the approach based onthis assumpproblem density futtion Tarbell (1989). With this tion, in a stoichiometric mixture, the single-point PDF of the prob em onsder d b D u ta nd T rbel ( 989 .…”

“…In a recent article, Dutta and Tarbell (1989) made a comFormulations and Model Presentation parative study of several turbulence closures for predicting the With the assumption of an infinitely fast chemistry, all the mean rate of reactant conversion in a chemical reaction of the pertinent statistics of the reacting field are related to those of type A + B--products in homogeneous turbulent flows. In this prietsaitc fteratn il r eae otoeo wre u roc ts in the aprb ase d on an appropriate conserved scalar variable, hereby denoted by work, we use recent developments in the approach based onthis assumpproblem density futtion Tarbell (1989).…”

“…The most general form (1989), several other closures are also considered. These are of the model can be expressed by the evolution equation (Pope, the PDF methods based on the generalized coalescence/dis-1982; Kosaly and Givi, 1987;Dutta and Tarbell, 1989): persion (C/D) models and those based on "assumed" frequencies. For the C/D models, the closures of Curl (1963), are examined.…”

“…Therefore, based on Eq. problem discussed by Dutta and Tarbell (1989), we consider 1, if the PDF of the conserved scalar is known, all the statistical a stoichiometric mixture with initially segregated reactants. information regarding the reacting scalars A and B is available.…”