Identification of wavemaker region in swirling flows using complex network analysis

Precessing vortex core oscillation (PVC) is a self-excited flow oscillation observed in strongly swirled flows that show vortex breakdown. When these oscillations occur in technological applications such as combustor nozzles in gas turbines and aircraft engines, they can significantly alter combustor operation by impacting unsteady flame dynamics, fuel-air mixing and emissions. Prior work has shown that the PVC is caused by the precession of the vortex breakdown bubble (VBB). The flow region responsible for the generation of PVC oscillations is referred to as the wavemaker. Changes to the flow in the wavemaker region can induce or suppress the PVC oscillations. This region in the flow can be identified as the region where changes to the time-averaged mean flow have a large quantitative impact on the eigenvalue of the PVC mode (structural sensitivity) and can be derived from direct and adjoint linear stability analysis. This analysis while useful can realistically be performed in simple geometries that are axisymmetric or two-dimensional. Also, prior studies have shown that this approach requires accurately estimating time-averaged flow fields from CFD methods such as LES or RANS. In this paper, we present a data-driven approach using complex network theory to determine the shape and position of the wavemaker region associated with the PVC in a swirl nozzle using time series LES data. We present results from networks constructed using two measures of node connectivity that use correlation and mutual information between radial velocity fluctuations at various points in the flow field. The wavemaker is identified using points with high weighted closeness centrality. The results show that the wavemaker is positioned upstream of the breakdown bubble and extends into the swirl nozzle. These results agree well with the predicted position and extent of the wavemaker for the same flow configuration, obtained using structural sensitivity with mutual information giving a better match. The network analysis also shows that the wavemaker disappears when a centrebody is introduced due to the wavemaker region being disrupted. A windowed network analysis of the configuration with the centrebody shows an intermittent appearance and disappearance of the wavemaker region, coinciding with intermittent epochs of PVC oscillation. These results show that complex network analysis can be applied effectively to extract wavemaker information from time series data of turbulent fluid flows.