Discrete dynamical system models of turbulence-chemical kinetics interactions

An approach to subgrid-scale (SGS) modeling for large-eddy simulation of turbulent non-premixed combustion is proposed and tested against experimental data. The model is composed of three specific factors: an amplitude, an anisotropy correction and a temporal fluctuation to be evaluated at each discrete point, during each time step, of resolved-scale calculations. We employ discrete dynamical systems (DDSs) for the third factor and in the present work focus on construction of these for a reduced kinetic mechanism and compare results with experimental data from the Technische Universitat Darmstadt H₂/N₂-air jet diffusion flame H₃. The DDS model is derived as a single-mode Galerkin approximation (with the mode left arbitrary) of the governing partial differential equations, but with the mode number and normalization (s) incorporated into bifurcation parameters. Such algebraic systems are capable of producing the full range of temporal behaviors of the original differential equations (while being very efficient to evaluate) and, in particular, can exhibit the chaotic behavior of fractal (strange) attractors that can be associated with turbulence. Moreover, they are able to mimic specific reaction pathways for any given kinetic mechanism on the subgrid scales. We compare computed results from the SGS model with the above mentioned data, both qualitatively (appearance of the time series) and quantitatively (rms fluctuation levels) and show reasonable agreement, especially for the former.