Numerical Simulation of the Deflagration to Detonation Transition in Granular High-Energy Solid Propellants

Abstract

This paper describes a one-dimensional code developed for analyzing the two-phase deflagration to detonation transition (DDT) phenomenon in granular high-energy solid propellants. The deflagration to detonation transition model was established based on a one-dimensional two-phase reactive flow model involving basic flow conservation equations and constitutive relations. The whole system was solved using a high resolution 5th-order WENO (Weighted Essentially Non-Oscillatory) scheme for spatial discretization, coupled with a 3rd-order TVD Runge-Kutta method for time discretization, to improve the accuracy and prevent excessive dispersion. An inert two-phase shock tube problem was carried out to access the developed code. The DDT process of high-energy solid propellants was simulated and the parameters of detonation pressure, run distance to detonation and time to detonation were calculated. The results show that for a solid propellant bed with solid volume fraction 0.65, the run distance to detonation was about 120 mm, the detonation induced time was 28 μs, and the detonation pressure was 18 GPa. In addition, the effects of solid volume fraction (φs) and pressure exponent (n) on the deflagration to detonation transition were also investigated. The numerical results for the DDT phenomenon are in good agreement with experimental results available in the literature. IntroductionStudy on the deflagration to detonation transition (DDT), which is one of the important characteristics of energetic materials, has been conducted for many decades, in both industrial and military studies. This phenomenon is a complex solid combustion problem and is influenced by a variety of factors. DDT has been physically investigated by typical Macek's tube experiments [1,2] and piston-ignited DDT experiments [3][4][5] in order to obtain a mechanistic description of the phenomenon. Bernecker [6] reviewed the DDT process and the variables that influence it in porous high-energy propellants. Recently, McAfee [7] summarized many of the physical observations of the DDT process and systematically elucidated the DDT mechanism for energetic materials with different densities, defining the major types of DDT. However, it is difficult to describe the transition to detonation accurately and quantitatively because of the complex nature of the DDT process. Therefore, the present paper attempts to study the DDT process of a high-energy solid propellant by numerical simulation, in order to provide the basis for the safe production, storage and use of propellants.At present, three main reactive flow models, varying from single phase to three phases, have been developed to simulate the deflagration to detonation transition in granular energetic materials [8][9][10][11]. Two-phase flow models, including the Baer-Nunziato (BN) model proposed by Baer, Nunziato et al. [12,13] and the Powers-Stewart-Krier (PSK) model proposed by Powers et al. [14], are widely used to numerically simulate the DDT process of an energetic material. The two-phase flow models are ba...