Hydrodynamic Instability of a Premixed Flame Under Confinement

A linear stability analysis has been performed to identify the role of the hydrodynamic instability when combustion occurs in a closed tube. The model treats the flame as a surface of discontinuity in an otherwise inyiscid isentropic mixture. The burning rate is obtained from an analysis of the internal flame structure. It is shown that flame acceleration, a consequence of pressure buildup, has a damping influence on the long wavelength disturbances. Disturbances of shorter wavelengths grow but their growth rate exceeds the propagation speed, which can only then be identified as an instability. The growth rate is found to be always lower than the corresponding growth rate for a freely propagating flame.