Coupling of harmonic flow oscillations to combustion instability in premixed segments of triple flames

Combustion instability of a lifted triple flame downstream of the injector nozzle in an acoustic field is studied, with implication on the combustion instability in liquid rocket engines. The analysis is focused on the premixed flame segment, and is based on the linear equation for a perturbed flamefront. Assuming that the radius of the flamefront curvature is much larger than that of the internal flame structure, the premixed front is approximated as being quasi-planar. Both acoustical stabilization of the hydrodynamic flame instability and excitation of the parametric instability by sound waves are considered, and the limitation for stable/unstable regimes as a function of flame parameters and acoustic frequency/intensity is determined. The velocity-wise nature of the sound is scrutinized, namely, the acoustics are imitated by a pocket of harmonic flow oscillations. First, the Landau limit of infinitely thin flames is employed. Then the formulation is extended to account for the finite flame thickness, and it is demonstrated how unstable regimes are modified by the flame thickness.