Identification and Dynamics of Coherent Structures in Double-Stage Swirling Flows Utilizing the Unsteady Reynolds Averaged Navier–Stokes and Large Eddy Simulation Methods

Abstract To study the coherent structure within a combustion chamber equipped with a double-stage swirler, unsteady Reynolds averaged Navier–Stokes (URANS) of realizable k–ε and renormalization group (RNG) k–ε, along with large eddy simulation (LES) are employed. The time-averaged results indicate a notable degree of consistency among the three turbulence models and the experimental data. Analysis of instantaneous streamlines and Q criterion isosurfaces reveals that the unsteady realizable k–ε exhibits poor predictive capability. In contrast, the unsteady RNG k–ε shows slight improvement, although its ability to predict small broken vortex structures remains inferior to that of LES. Fast Fourier transform (FFT) analysis indicates that the unsteady RNG k–ε and LES yield relatively consistent characteristic frequency of 560 Hz and 556 Hz of the precessing vortex core (PVC) at Re = 16,273, and 1109 Hz and 1121 Hz at Re = 32,547, while the unsteady realizable k–ε fails to provide a reasonable prediction frequency of it. Additionally, the modal evolution and spiral precession downstream along the shear layer (SL) are captured by the first mode of LES and the unsteady RNG k–ε using the spectral proper orthogonal decomposition (SPOD) method, while the unsteady realizable k–ε predicts unstable structures such as vortex breakup in the flow field. Both unsteady realizable k–ε and unsteady RNG k–ε's second modes characterize the vortex shedding process, whereas LES's second mode reveals the existence of mode pairing phenomenon.