Acoustic parametric instability of non-planar premixed flames: Extension of wavenumber-based Markstein numbers via N₂ dilution

Self-excited thermoacoustic parametric instabilities in downward-propagating laminar premixed flames are studied experimentally and analytically. Propane-air flames were propagated in an open-closed combustion tube to capture the spatiotemporal flame evolution in transition to acoustic parametric instabilities. The wavenumber response of the vibrating flame, initially planar, from parametric resonance is measured to derive the Markstein number. The Markstein number is determined by employing a thin laminar flame model under acoustic flow-field excitation governed by one-step, high-activation-energy Arrhenius kinetics whose analytical functions are reduced into a Mathieu equation. To promote flame planarization, N₂ dilution is introduced for stoichiometric and rich propane-air flames which exhibit complete instability across the range of acoustic intensities tested in the experiments. Experimental results show that the wavelength of cellular flames at the onset of parametric instability is primarily influenced by stoichiometry rather than N₂ dilution. However, the Markstein number decreases with increasing N₂ dilution due to the corresponding reduction in flame temperature. For completely unstable flames, Markstein numbers are extrapolated based on the gas expansion coefficient. This work highlights the relative importance of temperature-dependent diffusivities, gas expansion coefficient and effective Lewis number on the derived value of the Markstein number; however, the Markstein number alone is not sufficient to characterize flame stability. The values obtained in this study are compared with Markstein numbers relative to fresh gases from various experimental methods reported in the literature.