Computational simulation of nonlinear L* Combustion instability in solid rockets

L* instability in solid rocket motors is numerically modeled using a simplified kinetics combustion model coupled with a simplified L* combustor. A nonlinear combustion model (WSB) is used with low activation energy, bimolecular single-step reaction in the gas phase and high activation energy, zero-order decomposition in the condensed phase. Quasi-steady gas and condensed phase reaction (surface reaction) were assumed. The phenomenological Zeldovich-Novozhilov (ZN) approach was used. Classical linear L* analytical results are recovered. Several nonlinear behaviors are predicted computationally, many of which are similar to observed nonlinear L* instability behavior such as extinction, chuffing, limit-cycle (amplitude-limited) oscillations, and frequency shifting. Frequency shifting (or dual frequency oscillation) has been observed experimentally in double base propellant but attributed tentatively to the two-stage flame structure of these propellants. In the present model, dual-frequency behavior is manifested without including a two-stage flame structure.