Tri-Global stability analysis of reacting, swirling flows*

Swirling jets are used as canonical flow fields in combustion systems with the well-established advantage of a swirl-stabilized flame. Modeling unsteady vortical hydrodynamic structures is considered a serious challenge for swirling flows in literature as the structures significantly perturb the flame. Hydrodynamic stability analysis has been a prominent, efficient, yet developing technique for low order modeling of coherent structures for the past few decades. The objective of this study is to develop a reduced order model by means of a Tri-Global hydrodynamic stability framework to identify self-excited natural hydrodynamic modes of a LES mean flow based on a commercial nozzle. Tri-Global linear stability analysis is employed by exploiting the sparsity patterns of linearized Navier Stokes equations through a high accuracy, centered finite difference scheme. Upon discretizing the linearized governing equations about a 7-point stencil, a generalized-eigenvalue problem is formulated leading to a sparse stiffness and mass coefficient matrices for a structured 20x20x20 cubical grid. The GEVP is solved using a shift-and-invert technique to detect global unstable modes with high growth rates of the mean-flow in a low-frequency search region. A helical mode decomposition is carried out to extract the azimuthally periodic helical modes commonly associated with swirling jets. Lastly, a comparison between Bi-Global and Tri-Global stability analyses is shown to understand effects of varying modal characteristics from two to three dimensions.