Accessed Compositions in Turbulent Reactive Flows

At a given position and time in a turbulent reactive flow involving many chemical species, the thermochemical composition corresponds to a point in the multi-dimensional composition space. The union of all such points, for all positions, times and realizations, is defined to be the accessed region of the composition space. The geometry of the accessed region is investigated from several perspectives. Many existing models of turbulent nonpremixed combustion (e.g., equilibrium chemistry, the steady flamelet model, and the conditional moment closure) implicitly assume that the accessed region is a low-dimensional manifold of dimension one or two. It is shown from the conservation equations that the simultaneous actions of mixing and reaction can lead to an accessed region of significantly higher dimension than occurs when mixing and reaction act separately or sequentially. For a laminar flame, the accessed region is a curved manifold of the same dimensionality as the flow; whereas for a turbulent reactive flow it is a plane manifold, generally of higher dimension. Several processes are identified which can lead to the edge of the manifold being nonconvex.