(531g) Dimension Reduction in Turbulent Combustion Modeling

Modeling turbulent combustion processes requires solution of a large number of equations due to the large number of reacting species present. Furthermore, the computational cost of resolving turbulent flows scales as Re3. Reducing the range of scales that must be resolved as well as the number of equations to be solved is, therefore, of utmost importance to achieve simulations of practical combustion systems.

In this paper, we address a method to reduce the number of species equations that must be solved via application of Principle Component Analysis (PCA). This technique provides a robust methodology to reduce the number of species equations by identifying correlations in state-space and defining new variables that are linear combinations of the original variables. We show that applying this technique in the context of Large Eddy Simulation allows for a mapping between the reduced variables and the full set of variables that is insensitive to the size of filter used. This is notable since it provides a model to map state variables to progress variables that is a ?closed? model.

As a linear transformation, PCA allows us to derive transport equations for the principal components, which have source terms. These source terms must be parameterized by the reduced set of principal components themselves. We present results from a priori studies to show the strengths and weaknesses of such a modeling approach. Results suggest that the PCA-based model can identify manifolds that exist in state space which are insensitive to filtering, suggesting that the model is directly applicable for use in Large Eddy Simulation. However, the resulting source terms are not parameterized with a high degree of accuracy.