Study of the Spatio-Temporal Dynamics in the Volvo Validation Rig Using Modal Decomposition Techniques

Turbulent premixed combustion is governed by coupled, nonlinear, and multi-scale interactions of turbulence, heat release, and variations of thermochemical properties, giving rise to highly unsteady flow dynamics. Characterizing the dominant large-scale spatially coherent structures and their temporal features is essential for understanding the coupling of flame with the flow field, diagnosing hydrodynamic or thermoacoustic instabilities, and developing reduced-order models. In this study, we employ proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and spectral POD (SPOD) techniques to investigate the spatio-temporal dynamics of a statistically stationary turbulent premixed flame. We analyze high-fidelity large-eddy simulation (LES) datasets of the Volvo combustor under non-reacting (cold) and reacting conditions. POD is used to extract the most energetic coherent structures and quantifies the effects of heat-release on the spatial organization of these structures. DMD is used to isolate frequency-resolved spatially coherent motions and identify dynamically significant oscillatory behavior linked to shear-layer instabilities and flame-flow interactions. SPOD is used to isolate dominant frequency-resolved modes suitable for statistically stationary flows. Modal analysis revealed that while the non-reacting flow exhibited broadband hydrodynamic activity across $St \approx 0.48 - 1.15$, the reacting flow showed sharply amplified, combustion-induced coherent oscillations clustered near $St \approx 0.9$. SPOD further confirmed energetic peaks in this same frequency band. By jointly applying these complementary modal decomposition techniques, this study provides a comprehensive assessment of their capabilities in resolving coherent motions, quantifying modal energy distribution, and capturing unsteady dynamics across operating regimes.