Effect of flame surface area of downward propagating flames induced by single and double laser irradiation on transition to parametric instability

The single laser irradiation (SLI) method was adopted to develop a double laser irradiation (DLI) method to investigate the effects of laser-induced structures of downward-propagating flames in a tube on the transition from primary acoustic instability to parametric instability. Previously, the SLI method was effectively used to study the interaction between acoustic oscillation and flame structure by controlling the shape of the flame front. The deformed cellular structure (either concave or convex) of the SLI-induced flame can transition from primary acoustic instability to parametric instability under certain conditions. We conducted experiments in the same combustion tube with C₂H₄/O₂/CO₂ mixtures using both SLI and DLI for comparison. The DLI method forms double cellular structures, while SLI only forms single cellular structures on the flames. It was found that the DLI method was more effective than SLI in generating transition to parametric instability under same total laser power. Furthermore, a linear relationship was found between the area of the deformed structure (irrespective of its dimension) and the corresponding growth rate of acoustic pressure fluctuation during the propagation of the deformed flame. SLI- and DLI-induced deformed structures having the same deformed surface area demonstrate the same growth rate of thermo-acoustic instability regardless of the difference in (ak)², where a is the amplitude and k is the wavenumber of the deformed structures, respectively. This factor described in the velocity coupling mechanism is important to reveal the growth rate of thermo-acoustic instability due to the variation in the flame surface area. The results revealed that the actual flame surface area, rather than (ak)² of the laser-induced downward-propagating flame structure, determines the transition in the presence of nonhomogeneous cell distribution induced by SLI and DLI. The total deformed surface area is a more comprehensive criterion for transition to parametric instability.