Reduced-Order Modeling and Validation of Vortical Modes in Swirling Flows

Swirling jets are canonical flow fields in combustion systems, offering advantages such as flame stabilization and enhanced turbulent mixing. One of the key industrial challenges in utilizing hydrodynamically unstable swirling flows is accurately modeling large-scale, organized vortical structures. The interaction between flow fluctuations, unsteady heat release, and acoustic oscillations can lead to detrimental combustion instabilities. This study investigates the vortical dynamics of a high-fidelity turbulent LES swirling flow field. Coherent structures are characterized by extracting unstable global hydrodynamic modes from the time-averaged flow. Results are compared using two widely used modal decomposition techniques: snapshot proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), both of which identify and characterize coherent structures in turbulent flows. Snapshot POD provides an energetically optimal representation of the flow, where spatially orthogonal modes are ordered according to their turbulent kinetic energy (TKE). In contrast, DMD identifies the dominant dynamics through a spectral decomposition of the temporal flow evolution, yielding a series of spatial modes each associated with a distinct oscillation frequency and growth or decay rate. Visualizations of high-energy POD modes and dominant dynamic modes reveal several axisymmetric and helical vortex shedding structures. A power spectral density of the POD time coefficients identifies the dominant frequencies associated with the POD modes, while the DMD spectrum directly provides the temporal characteristics of each dynamic mode.