Numerical simulation of hypervelocity projectiles in detonable gases

Abstract

A numerical scheme for calculating hypersonic flows involving shock-induced combustion is discussed. The analysis is limited to inviscid flow and includes chemical nonequilibrium and real-gas effects. Two types of flows are considered. First, the hypersonic, exothermic blunt-body flow problem is examined for mixtures of Hi/Oi and Hi/air, and the numerical results are compared with experimental results. Second, a hypervelocity mass launcher concept known as the is investigated in the velocity range of 5-7 km/s. Temperature contours and the distribution of various physical quantities along the ram accelerator projectile surface and tube wall are presented for a 14-deg nose projectile and for a gas mixture of 2Hi + Oi + 5He. In the present study, a new numerical scheme developed for calculating hypersonic chemically reacting flows is described. The new numerical formulation represents a departure from previous computational fluid dynamics models of the ram ac- celerator.11'12 The earlier models were based on a global Arrhe- nius rate equation, with the Arrhenius constants determined from experimental ignition delay studies. The current model is more accurate in that it accounts for the reaction kinetics of a 7 species 8 reaction combustion model. Nonetheless, the ear- lier results were encouraging in that they predicted hyperveloc- ity operation was possible. The new scheme, based on an algorithm developed by Yee and Shinn,13 was applied to spheres moving through mixtures of H 2/O2 and H2/air at speeds above and below the corre- sponding Chapman-Jouguet detonation speed. The results were then compared with the experiments just mentioned. The code was also used to investigate the flow and combustion processes in the ram accelerator, in the velocity range of 5-7 km/s. The first section of this paper presents an overview of the phenomena associated with hypersonic exothermic blunt-body flow. The following sections describe the governing equations, combustion model, and the numerical scheme used. Finally, results are presented for hypersonic blunt-body flows and for a complete ram accelerator configuration. Regimes of Exothermic Blunt-Body Flow Figure 2 shows the structure of the shock layer in the vicinity of the stagnation point of a blunt body moving through a detonable gas mixture. At flight speeds t/i, sufficiently low such that the temperature behind the bow shock is less than the ignition temperature, no combustion will occur. At higher flight speeds, but still below the detonation speed D of the gas mixture, the shock and combustion front are separated by an induction zone of thickness A/. This situation is shown in Fig. 3, obtained from the work of Lehr, 10 for a stoichiometric