Determining strong thermoacoustic coupling directions in Helmholtz combustors using time series causality analysis

The large amplitude pressure oscillation generated in the operation of various combustion systems results from the coupling of heat release and acoustics. This coupled system includes two-way causality, namely how heat release and pressure affect quantitatively each other. Regarding this issue, the majority of studies have focused on how heat release affect pressure. This research seeks to identify the strong coupling direction in Helmholtz combustors under thermoacoustic coupling conditions, or whether the influence of heat release fluctuations on pressure fluctuations is equivalent to the influence of pressure fluctuations on heat release fluctuations, and this two-way causality is identified quantitatively by convergent cross mapping. Experimental measurements of both heat release and pressure fluctuations were obtained using a Helmholtz-type combustion system. Then the causality analysis between the series is performed by convergent cross mapping. The results demonstrate the variation of heat release fluctuations is mainly driven by the variation of acoustic pressure and vice versa. While the influence of pressure fluctuations on heat release fluctuations is greater than the influence of heat release fluctuations on pressure fluctuations, and the coupling between heat and acoustics in thermoacoustic instability is inconsistency. Notably, the influence of heat release on pressure is magnitude-dependent: it strengthens under low heat release conditions and weakens as heat release increases. These phenomena are illustrated from the perspective of Rayleigh's criterion, and when the phase difference between heat release and pressure equals 0°, the influence of heat release on pressure reaches its peak. Based on this property, the injector distance is altered to improve the influence of heat release on pressure.