Global hydrodynamic stability of swirling jets

Swirling jets are canonically used in reacting flow systems with the well-known application of the swirl-stabilized flame. However, swirl induced flows often give rise to unsteady vortical, hydrodynamic structures. In combustion, these unsteady structures couple with combustor acoustics and heat release oscillations to cause the well-known thermoacoustic instability. Thus, accurate and efficient modeling of the unsteady hydrodynamic structures presents a serious challenge in current thermoacoustic systems literature.

Hydrodynamic stability analysis has emerged as a prominent tool to model linear, first order coherent dynamics of spatio-temporal flows in the past few decades. In this work, different techniques of linear stability, with modal characteristics varying across multiple dimensions, will be explored for swirling flows varying spatially across multiple coordinates. This study aims to detect unstable modes of swirling base-flow data at constant swirl number in two different frameworks: Bi-Global and Tri-Global stability. The methods used for both frameworks are established with a strictly global approach to study self-excited natural hydrodynamics of the flow. The computational cost associated with varying modeling fidelity from 2-D to 3-D is also considered in this study. Secondly, the validation of unstable modes detected by linear stability is done by comparison with high energy-ranked Proper Orthogonal Decomposition (POD) modes. Lastly, an extension to this study is considered by testing the established frameworks for an independent base-flow in a confined geometry that is parameterized by swirl number.