  The response to small perturbations of the Sandia CH4/air flame series is
studied using a dynamical systems formula- tion. Here, the Sandia D and E
turbulent partially-premixed flames are computed using large eddy simulation
(LES) with a flamelet/progress variable approach. Using 300 simultaneous LES
computations of each flame, the partial Lyapunov spectrum of the flow is
obtained, which provides a set of Lyapunov exponents (LEs) and Lyapunov vectors
(LVs). Special numerical procedures to handle such large data sets and perform
matrix manipulations on-the-fly are discussed. From the LEs, the dimension of
the attractor for the flames was estimated, for the first time, to be at least
5000 (flame D) and 10500 (flame E). This is a significant result indicating
that the chaoticity of the turbulent flame is confined to a volume of
phase-space that is quantified. The growth of perturbations occurs at
time-scales that are much larger than the smallest strain-rate based times
scales, but smaller than the integral scales. Further, the Lya- punov vectors
that determine the perturbation response show that the strongest perturbations
are aligned with the jet breakdown region, while other LVs are aligned with the
shear layer. It is found that both the extinction/re-ignition process and the
turbulence-induced jet motion strongly contribute to the flame chaoticity but
are not equally important for all the LVs. These results provide new insights
into the perturbation response of turbulent flames. More broadly, this Lyapunov
approach allows a full characterization of the chaotic dynamics associated with
turbulent flames, which have applications for both modeling and control of such
complex flows.
