Several modes of ram accelerator propulsion have been investigated experimentally and theoretically by the authors and their colleagues. One of these propulsive cycles is the thermally choked ram accelerator mode (Fig. 1a), which operates with in-tube Mach numbers typically ranging from 2.5 to 4 and at projectile velocities below the Chapman-Jouguet (CJ) detonation speed of the propellant mixture (Hertzberg et al. 1988, 1991; Bruckner et al. 1991). In this mode the thrust is provided by the high projectile base pressure resulting from a normal shock system that is stabilized on the body by thermal choking of the flow at full tube area behind the projectile. The thermally choked propulsive mode can be modeled using a simple one-dimensional theoretical approach (Bruckner et al. 1991; Knowlen and Bruckner 1992). This model predicts that the normal shock recedes along the body as the projectile Mach number increases. In the hypothetical case where the projectile tail tapers to a point and the flow is inviscid, the normal shock gradually falls back to the full tube area. A normal shock in a constant area duct, followed by heat addition and thermal choking in steady flow, constitutes a CJ detonation wave. Thus, theory predicts that the thrust goes to zero as the projectile velocity approaches the CJ detonation speed of a given propellant mixture. In order to achieve velocities higher than the CJ speed of a particular mixture, the ram accelerator tube can be subdivided into several sections, called stages, each of which is filled with a different propellant mixture, such that the acoustic and detonation speeds of the mixtures increase towards the muzzle. In this manner the projectile can be constrained to operate within a favorable Mach number range in each stage, and the ultimate velocity of the projectile is governed by the characteristics of the final stage.
It has been experimentally observed that the thrust as a function of Mach number is accurately predicted by the one-dimensional theoretical model of the thermally choked propulsive mode at velocities up to approximately 85% of the CJ detonation speed of the propellant mixture. At higher projectile velocities, however, the thrust typically begins to exceed that predicted by the theoretical model, reaching a relative minimum at velocities near 95% CJ speed, and then tends to increase with increasing velocity (Burnham et al. 1990; Hertzberg et al. 1991). This anomalous behavior (in the context of thermally choked theory) coincides with the experimental observation of combustion activity occurring on the projectile body. Figure 1b shows generalized heat addition regions located on and behind the projectile that could contribute to the thrust at velocities near the CJ speed. Experiments have shown that in this "transdetonative" velocity regime (typically Mach 4 to 6), the projectile can accelerate smoothly from velocities below to above the CJ speed of a propellant mixture. This transdetonative behavior was an unexpected experimental finding that has significant implications for enhancing the muzzle velocity of single-stage ram accelerators and reducing the number of propellant mixtures required in multi-stage facilities.
For accelerating projectiles at even higher Mach numbers several "superdetonative" ram accelerator modes have been investigated both theoretically and experimentally (Knowlen et al. 1987; Bogdanoff and Brackett 1988; Kull et al. 1989). These modes operate at velocities greater than the detonation speed of the propellant mixture. One proposed supersonic combustion process involves shock-induced combustion, wherein the propellant mixture is ignited by one of several reflected oblique shock waves within the flow region between the projectile and tube wall, as shown in Fig. 1c. The supersonic heat release raises the gas pressure on the afterbody of the projectile, resulting in thrust as the reacted propellant expands back to full tube area. Other combustion processes capable of providing thrust at superdetonative velocities have also been suggested, such as oblique detonation cycles and mixed-mode combustion cycles (i.e., heat addition processes that occur in both subsonic and supersonic regions of the flow field). Superdetonative operation can, in principle, accelerate projectiles to nearly three times the detonation speed of hydrogen-oxygen propellant mixtures, i.e., to velocities in excess of 8 km/sec.
The thermally choked propulsive mode has been experimentally investigated at velocities of 0.7 to 2.7 km/sec and Mach numbers of 2.5 to 4. Transdetonative experiments have accelerated projectiles, which were initially propelled by the thermally choked mode, to exit velocities corresponding to Mach 6.5 in methane-based propellant mixtures, achieving single-stage velocity gains as high as 1 km/sec. Many different propellant mixtures have demonstrated the ability to accelerate projectiles smoothly through their respective CJ detonation speeds to superdetonative velocities. Exploratory experiments conducted entirely in the superdetonative velocity range of an ethylene-based propellant mixture have demonstrated positive thrust at Mach numbers up to 8.5, which corresponds to a maximum velocity equal to 150% CJ speed. Data from investigations on the three propulsive modes indicate that the acceleration performance in each velocity regime is characterized by distinctively different pressure and luminosity phenomena which provide clues as to the nature of these propulsive cycles (Hertzberg et al. 1991).