Global Stability and Forced Response Analysis of Swirling Flows in Aviation Combustors

Swirling jets are canonical flow fields used to stabilize flames in many gas-turbine combustion systems. These flows amplify background acoustic disturbances and perturb the flame, producing combustion noise and potentially combustion instabilities. Hydrodynamic flow response to acoustic excitations in reacting flows is an important modeling task for understanding combustion noise and combustion instabilities. This study utilizes a global hydrodynamic stability analysis in a biglobal and triglobal framework to model the vortical hydrodynamic modes of a reacting, swirling large eddy simulations (LES) mean-flow based on a commercial nozzle. After conducting an unforced, natural biglobal stability analysis to study the unstable eigenmodes of the flow, linearized equations of motion are used to study flow response of the flow to forcing. An empirical velocity transfer function is constructed by determining the flow response to a harmonically varying $150−1500$ Hz $u′$ velocity disturbance at the inflow boundary. These disturbances are strongly amplified, with amplification factors ranging from about 20 to 50 and peaking at about 1050 Hz, or $St=0.375$⁠. A comparison study with a Cartesian, three-dimensional (3D) reacting base-flow is also performed where the base-flow varies spatially in three-dimensions. The study utilizes a stable, high accuracy, but computationally effective centered finite difference scheme based on a three-dimensional structured mesh. Illustrative results present the qualitative modes and quantitative transfer functions for Biglobal and Triglobal stability analyses.