Interacting Linear Modes in the Turbulent Flow of an Industrial Swirled Combustor

Swirled flows often feature global modes that become manifest as skew-symmetric helical vortices, also known as precessing vortex cores, which dominate the flow dynamics. This study uses linear stability analysis (LSA) and bispectral mode decomposition (BMD) to elucidate the interactions of such modes in the turbulent, nonreacting, swirled flow of an industrial, three-passage, aeroengine fuel injector obtained via large-eddy simulation. A discrete Fourier transform in time retrieves the modes as narrow-banded, evenly spaced peaks in the spectral amplitude of the turbulent signal, where the second mode is dominant. Similar arrangements are known to appear as a consequence of a saturated global mode, which amplifies its higher harmonic frequencies due to nonlinear effects. We show that each mode appears in the spectrum of LSA eigenvalues, indicating that the subdominant peaks are caused not only due to nonlinear interactions but that they have an underlying linear mechanism. A structural sensitivity analysis based on the adjoint LSA shows that the observed helical modes originate close to the exit plane of the fuel injector. Finally, the BMD reveals significant nonlinear interaction between the individual modes. It is hypothesized that this interaction amplifies the modes, which are linearly stable, leading to the strong dynamics in the flow.