Direct Numerical Simulation and Simple Closure Theory for a Chemical Reaction in Homogeneous Turbulence

The direct numerical simulation of turbulent flows serves as a useful test of simple closure theories, since one can examine the dynamics of the concentration and veloCity fields in more detail than in laboratory experiments and learn how the interaction of turbulent motion and molecular diffusion affects the overall reaction rate. A brief review of the most popular methods available for full turbulence simulations is presented, and a demonstration of the usefulness of direct numerical simulation is given for simple single-point closure theories (viz., those of Toor and of Patterson) applied to the irreversible, second-order chemical reaction of initially unmixed reactants.