Data-driven reduction and decomposition with time-axis clustering

Abstract

A new approach for modal decomposition through re-interpretation of unsteady dynamics, termed time-axis clustering, is developed in this work and is demonstrated on an experimental turbulent reacting flow dataset consisting of simultaneously measured planar OH-PLIF and PIV fields in a model combustor. The method executes a K-Means clustering algorithm on an alternative representation of the input snapshot dataset: the dataset is interpreted here as a collection of one-dimensional time series, where each time series represents the time evolution of some flow quantity of interest (QoI) at a fixed point in physical space (i.e. pixel locations). The clustering algorithm in the modal decomposition context produces (a) spatial modes (called time-axis modes) that identify localized regions of dynamical similarity in physical space and (b) temporal coefficients that represent average trajectories of the flow QoI conditioned on the regions in physical space identified by the corresponding spatial mode. Due to the non-overlapping nature of K-Means clusters, visualization of the modes provides a unique pathway for flow feature extraction based on dynamical similarity. Ultimately, this work shows how time-axis clustering provides a promising avenue for domain-localized data-based modelling of complex fluid flows.