Optimization of Proper Orthogonal Decomposition using Various Preconditioning Techniques to Analyze Autoignition Simulation Data of Non-Homogeneous Hydrogen-Air Mixtures

Abstract

The proper orthogonal decomposition (POD) method is implemented on unsteady 2D data from direct numerical simulations (DNS) of auto-ignition in non-homogeneous hydrogen-air mixtures. The analysis is implemented to evaluate requirements for the reproduction of transient, multi-dimensional and multi-scalar processes in combustion. The resulting low-order models may be used to store and manage large data sets for post-processing and visualization, and for the implementation of POD reduced data as an integral element of model-based closure in turbulent combustion. Data reduction is implemented on a set of thirty snapshots of 2D fields of the passive scalar: the mixture fraction, and reactive scalars: the reaction progress variable, the reactants, hydrogen (H2) and oxygen (O2), mass fractions and intermediate species, H-radical and HO2 mass fractions. The snapshots cover the evolution of the hydrogen-air mixture from induction to high-temperature combustion stages. POD analysis shows that there are different requirements to reproduce passive and reactive scalars depending on the degree of their spatial and temporal variations during the autoignition process and the statistical distribution. The mixture fraction, which is affected by the mixing process only, requires the least number of eigenmodes, and yields a sufficient representation of the original data with only four eigenmodes. The success of the POD reduction of the reactive scalars depends upon the distribution of the statistics of the original scalar. On average, the reactive scalars require at least six modes to reproduce the original data. A number of pre-processing strategies of the scalar fields are explored to reduce the number of required eigenmodes. The strategies are designed to reduce the temporal and spatial spans of scalar values. The results show that different pre-processing strategies may yield different outcomes for the passive and reactive scalars reduction process depending on the statistical distributions of these scalars.