Numerical analysis of laminar velocity-forced premixed slit flames using modal decomposition techniques

Abstract

The relation between Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD) and Flame Transfer Functions (FTF) is explored to gain further insight into the dynamics of two-dimensional laminar slit flames externally forced by velocity perturbations. The application of POD to the heat release rate fields suggests that the resultant modes can be split into two groups: the ones that are related to the displacement of the reactive sheet in the normal direction with regards to the flame front, and the ones that contain the local flame front distortions. The latter modes show preferential frequencies associated to the phase values of π, 2π and 3π of the FTFs, which can be related to the maximum gain value depending on the case. Furthermore, the results of the modal analysis seem to support that the flame tip dynamics can be conceptually modelled as a set of standing waves whose joint response can reconstruct a propagation in the normal flame front direction, generating also the temporal fluctuations of the spatially-integrated heat release in the domain. The DMD analysis shows the existence of an interaction between the flame and the flow, and illustrates the fundamental role played by the velocity perturbations at the base for the motion of the reactive sheet. Thus, the analysis shows how data-based decomposition methods can be used to identify complex physical phenomena contained in the FTF graphs with different levels of detail, and extend the modal analysis to the physical space.Novelty and significance statementThis paper proves the potential of modal decomposition techniques like POD and DMD to infer the underlying physics of canonical flames and their relation to the FTF, validating also the hypotheses and methodology of other reduced-order models in the literature. A canonical configuration featuring a two-dimensional slit flame has been selected to analyse the flame dynamics using these methods. Hence, this work aims to set the foundations to elaborate data-driven reduced-order models based on modal decomposition techniques to support the analysis and the study of flame dynamics.