Nonlinear dynamic combustion in solid rockets: L* effects

Nonlinear combustion and bulk-mode (L*) chamber gasdynamics in homogeneous solid propellant rockets are simulated computationally. A relatively new nonlinear simplified-kinetics combustion model is used. Quasi-steady gas and surface decomposition are assumed. Linear, oscillatory analytical results are recovered (as numerical validation). In general, the calculated results exhibit motor behavior in agreement with that observed experimentally for different L* values, as summarized by Price (Price, E. W., "L* Instability," Nonsteady Burning and Combustion Stability of Solid Propellants, edited by L. De Luca, E. W. Price, and M. Summerfield, Vol. 143, Progress in Astronautics and Aeronautics, AIAA, Washington, DC, 1992, Chap. 9, pp. 325-361) increases from low, < L*₀, to high, > L*₀, values burning rate and motor pressure go from erratic and/or oscillatory to steady and stable. Several nonlinear combustion phenomena that have been observed experimentally but that are beyond the capability of linearized models are also predicted. These include rapid initial (over-) pressurization, propellant extinction, and dual-frequency and limit-cycle oscillations. The results suggest that some of these combustion phenomena could be due to nonlinear (but still quasi-steady) dynamic burning and mass conservation effects within the classical bulk-mode framework rather than more complicated fluid and flame dynamic effects that have been proposed. In particular, the rapid rate of initial pressurization and the ignition spike commonly attributed to erosive burning may be due to nonlinear dynamic burning at low L*. Even without an overpressurization spike, it appears that the rapid pressurization rate in solid rockets is at least partly due to the inherent L* instability of the initial state where L* < L*₀(α > 0) because of large values of L*₀ at low pressures.