Spatial Dependence Analysis of Thermoacoustic Coupling Strength in Helmholtz Pulse Combustor Using Convergent Cross Mapping

Abstract This study investigates the spatial thermoacoustic coupling strength between heat release dynamics and acoustic pressure waves that drive high-amplitude combustion instabilities. Experimental measurements of pressure oscillations and spatially resolved heat release fluctuations were conducted in a Helmholtz-type pulse combustor. Through the application of convergent cross mapping – an advanced nonlinear state-space reconstruction technique for causal inference from time-series data, we quantitatively characterize the mutual interactions between acoustic pressure and local heat release dynamics. The results reveal an asymmetric coupling between the pressure fluctuations and heat release fluctuations. Although both contribute to thermoacoustic instability, pressure fluctuations have a markedly stronger causal effect on heat release fluctuations compared to the reverse influence. Spatial analysis demonstrates depth-dependent coupling characteristics, with strong bidirectional interactions at low insertion depth transitioning to predominantly unidirectional (pressure-to-heat-release) coupling at greater penetration depths, and this transition results from the change of Rayleigh's efficiency. These results provide new insights into the spatially localized mechanisms governing thermoacoustic instability development in confined combustion systems.