A Finite-Mode PDF Model for Turbulent Reacting Flows

Abstract

The recently proposed multi-environment model, R. O. Fox, 1998, “On the Relationship between Lagrangian Micromixing Models and Computational Fluid Dynamics,” Chem. Eng. Proc., Vol. 37, pp. 521–535. J. Villermaux and J. C. Devillon, 1994, “A Generalized Mixing Model for Initial Contacting of Reactive Fluids,” Chem. Eng. Sci., Vol. 49, p. 5127, provides a new category of modeling techniques that can be employed to resolve the turbulence-chemistry interactions found in reactive flows. By solving the Eulerian transport equations for volume fractions and chemical species simultaneously, the local concentrations of chemical species in each environment can be obtained. Assuming micromixing occurs only in phase space, the well-known IEM (interaction by exchange with the mean) model can be applied to close the micromixing term. This simplification allows the model to use micromixing timescales obtained from more sophisticated models and can be applied to any number of environments. Although the PDF shape doesn’t change under this assumption, the interaction between turbulence and chemistry can be resolved up to the second moments without any ad-hoc assumptions for the mean reaction rates. Furthermore, the PDF shape is found to have minimal effect on mean reaction rates for incompressible turbulent reacting flows. In this formulation, a spurious dissipation term arises in the transport equation of the scalar variances due to the use of Eulerian transport equations. A procedure is proposed to eliminate this spurious term. The model is applied to simulate the experiment of S. Komori, et al., 1993, “Measurements of Mass Flux in a Turbulent Liquid Flow With a Chemical Reaction,” AIChE J., Vol. 39, pp. 1611–1620, for a reactive mixing layer and the experiment of K. Li and H. Toor, 1986, “Turbulent Reactive Mixing With a Series Parallel reaction: Effect of Mixing on Yield,” AIChE J., Vol. 32, pp. 1312–1320, with a two-step parallel/consecutive reaction. The results are found to be in good agreement with the experimental data of Komori et al. and the PDF simulation of K. Tsai and R. Fox, 1994, “PDF Simulation of a Turbulent Series-Parallel Reaction in an Axisymmetric Reactor,” Chem. Eng. Sci., Vol. 49, pp. 5141–5158, for the experiment of Li and Toor. The resulting model is implemented in the commercial CFD code, FLUENT,1 and can be applied with any number of species and reactions.