Reduced-order characterization of spatiotemporal dynamics in merging buoyant diffusion flames

The nonlinear dynamics of interacting diffusion flames play a decisive role in flame synchronization, unsteady heat release, and the onset of combustion instabilities in practical combustors. In this work, the spatiotemporal evolution of three buoyant diffusion flames is experimentally investigated as a canonical surrogate for multi-injector flame interactions. High-speed imaging (250 fps) and shadowgraphy reveal self-sustained oscillations characterized by vortex roll-up, periodic contraction, and flame-sheet detachment. Proper orthogonal decomposition (POD) and spectral proper orthogonal decomposition (SPOD) are employed to extract reduced-order representations of the governing modes. POD analysis indicates that the first few modes capture the dominant coherent structures, with secondary modes resolving fine-scale instabilities and harmonic content. The associated temporal coefficients exhibit a fundamental frequency of approximately 11 Hz, with higher harmonics linked to vortex breakdown and energy cascading. Complementary SPOD analysis isolates frequency-resolved spatial modes that are orthogonal in both space and time, thereby identifying the coherent oscillatory mechanisms driving the instability. The synergy of POD and SPOD reveals the multiscale coupling between shear-layer vortices, heat release fluctuations, and flame-surface oscillations. These results advance the mechanistic understanding of merging flame dynamics and provide a physics-based framework for reduced-order modeling of unsteady multi-flame combustion systems.