Micromixing model for turbulent reacting flows

Rodney Fox, Department of Chemical and Biological Engineering, Iowa State University, Ames, USA

"Micromixing" is a term with a long history over which its meaning has evolved and even diverged according to the scientific community employing it. Nevertheless, in the context of turbulent scalar transport, its meaning is fairly precise and centers on the phenomenon of decay of scalar fluctuations due to molecular diffusion in a turbulent flow. For this reason, micromixing is often referred to as "molecular mixing" in the turbulence literature to emphasize its close relationship to molecular diffusion . a small-scale phenomenon associated with the diffusive range of the scalar energy spectrum. Conceptually, turbulence interacts with an inert and dynamically passive scalar field to create scalar gradients in the diffusive range (sometimes referred to as "stirring"), which are subsequently destroyed by molecular diffusion. This close coupling between the fluid dynamics at large scales and the molecular diffusion at small scales makes the formulation of "universal" micromixing models a challenge. For reactive or dynamically active scalar fields the difficulties are further compounded by the production of scalar gradient through other mechanisms.

In this course we will review the theory of micromixing models in the context of one-point velocity-scalar probability density function (PDF) methods. The advantages of formulating the scalar mixing problem in terms of a PDF method (as opposed to a moment method) are well known (especially for turbulent reacting flows), and we will give a brief overview of the relevant theory. In PDF methods, the micromixing term has a precise definition in terms of a conditional statistic . the diffusive flux of the fluctuating scalar conditioned on the values of the velocity and scalar(s). The principal challenge is then to find a "general" model for this term that is subject to a number of constraints (inherited from the properties of the diffusive flux) and so-called "desirable properties" that are consistent with experimental and direct-numerical simulation data (Fox 2003). We will look in detail into the origin and nature of these constraints and properties and discuss the various modeling approaches that have been used to develop micromixing models for turbulent reacting flows.

R. O. Fox, Computational Models for Turbulent Reacting Flows, Cambridge University Press (2003).