Unsteady combustion of solid propellants: Simplified kinetics modeling

Simplified kinetics will continue to play an important role in computational simulation of solid propellant combustion for the foreseeable future, particularly in simulating unsteady combustion. The first part of this article reviews some recent progress made in connection with the Multi-disciplinary University Research Initiative (MURI) on solid propellant combustion instability with regard to simplified kinetics modeling for steady and particularly unsteady combustion. For homogeneous energetic materials (HMX and NC/NG) simplified kinetics combustion models have developed to the point that macroscopic generic features (e.g., burning rate, temperature, reactant, product) can be described within the modeling approximations and a priori predictive capability is a reasonable expectation. For composite propellants, however, ability to describe essential macroscopic behavior of even steady burning-for example, burning rate sensitivity to pressure and initial temperature-is still limited by lack of understanding of kinetics. The second part of this paper reviews MURI program progress in measuring pressurecoupled frequency response function R_p which is the primary quantity for comparison between experiment and theory for unsteady combustion. The de facto standard method for measuring R_p in the U.S. still appears to be the T-burner. Several other techniques for measure R_p are being developed; however, the results by various techniques show significant variation in the results for the same propellant at the same conditions. There is still a need for new techniques that are quick, inexpensive, use small amounts of material, and have high spectral resolution. The main feature of measured pressure-responses for both homogeneous and composite propellants is a broad, low-frequency, solid-phase thermal relaxation response peak which occurs around a non-dimensional frequency of Ω ~ 5 to 20. For Ω < E_c/RT_s the response of various propellants at various pressures are correlated fairly well by the non-dimensional frequency Ω, which is based on quasi-steady (QSHOD) theory. The significance of E_c/RT_s is that this is the value of Ω where the quasi-steady assumption (specifically, the quasi-steady condensed phase decomposition zone) assumption breaks down. For E_c ~ 40 kcal/mol (HMX), E_cRT_s - 25. For E_c - 20 kcal/mol (AP), E_c/RT_s ~ 12. Thus breakdown of quasi-steady conditions begins near the response peak or at just slightly higher Ω-values.