Flame-driven subharmonic bifurcation in a multi-flame Rijke tube

Studies on combustion instability have shown that thermoacoustic systems can exhibit a wide range of dynamics beyond periodic limit cycle oscillations. This is primarily due to the nonlinear interaction between the acoustic field and the unsteady heat release rate from reactive flows. Owing to its simplicity in design, the Rijke tube has been a popular setup for exploring dynamic states in thermoacoustic systems. Previous studies have demonstrated that simple Rijke tubes with laminar flames can exhibit quasi-periodic oscillations and chaos, though the underlying physics of these complex dynamics remains unresolved. Many of these studies have used multi-hole burners, which create several closely placed flames. In this study, we present an experimental investigation to assess the role of individual flame dynamics on the overall combustion dynamics observed when a multi-hole burner is placed inside a Rijke tube. Using a pressure sensor and high-speed Mie scattering imaging, we quantified and evaluated the individual flame shapes in a seven-hole burner and their relationships with the ensuing pressure time series. By utilizing hydrogen and methane premixed flames and varying the hydrogen percentages from low to high, we observed that the system transitions from periodic oscillations to quasi-periodic oscillations and finally to half-integer harmonics at higher hydrogen percentages, where the system exhibited both fundamental frequencies and half-integer frequencies. We will explain this behavior by analyzing the dynamics of closely packed flames in multi-hole burners.