Extended proper orthogonal decomposition (EPOD) and dynamic mode decomposition (DMD) for analysis of mesoscale burner array flame dynamics

An analysis of mesoscale combustion dynamics based on Extended Proper Orthogonal Decomposition (EPOD) and Dynamic Mode Decomposition (DMD) is presented. These decomposition techniques can fully characterize and quantify dynamically relevant coherent structures in a complex flow field by projecting it onto a simplified dynamical system with significantly fewer degrees of freedom. Coherent structures are extracted from three different data sets (one numerical and two experimental) and appropriately attributed to dominant flame dynamics without a priori knowledge of the reactive flow field. Numerically-constructed images and laminar flame OH-PLIF images served to validate POD and DMD analysis and its application on combustion phenomenon, respectively. The comparison showed that the temporal DMD method could clearly separate each structure in the spatial and spectral senses. However, an examination of the POD modes and the spectrum curves of each POD coefficient convincingly demonstrated that the POD mode corresponding to the desired structure is contaminated by the other uncorrelated structures. Based on these validations, POD and DMD analysis using high-speed OH chemiluminescence images of mesoscale combustor array under two characteristic conditions (Steady and oscillatory flame) was successfully carried out. Dominant spatial structures and their energy contents in the recirculation zone or shear layer were accurately resolved with DMD. In addition to the global frequency response spectrum, DMD can provide detailed descriptions of spectrally pure coherent features that can be systematically correlated to underlying physics that drives combustion instability and provide a consistent interpretation. Although, POD analysis revealed similar results, there were limitations in terms of the information presented (no growth or decay rate) and the obvious existence of the undesirable contamination of the POD modes, as reflected in the interaction between the desired and uncorrelated structures. The findings presented in this study enable a step forward for experimental community in flame oscillation and combustion instability analysis. The key insight regarding complex interactions between acoustics, fluid mechanics and combustion will ultimately serve a critical role in developing detailed combustion instability models.