Equations of state for thrust modeling of ram accelerator at different bores

The ram accelerator is a propulsion concept based on using shock-induced combustion to accelerate projectiles traveling at supersonic speeds in a launch tube pre-filled with a gaseous combustible mixture. Extensive experimental studies have been carried out at laboratories around the world, in various size bore ram accelerator facilities, namely 38-mm-bore at the University of Washington, Seattle, WA, 30-mm-bore and 90-mm-bore at the French-German Research Institute, Saint Louis, France, 120-mm-bore at the US Army Research Laboratory, Aberdeen, MD, USA, and 25-mm-bore at the Tohoku University, Sendai, Japan. Depending upon the facility, the fill pressures used in experiments ranged from 1 MPa to 20 MPa. Several modes of ram accelerator propulsion have been investigated, one of which operates in the sub-detonative velocity regime; i.e., below the Chapman-Jouguet (CJ) detonation speed of the propellant. The experiments utilized similar projectile geometries, propellants (CH4, O2, N2), and fill pressures. Based on the unsteady, one-dimensional (1-D) modeling of the thermally choked ram accelerator, thrust calculations conducted using real-gas equations of state accounted for the compressibility effects of the combustion products. Equations of state based on generalized empirical and theoretical considerations are incorporated into the TARAM 1-D computer code to predict the combustion end state equilibrium conditions. A virial type, namely the Boltzmann EoS, has been extensively used and its applicability to the RAMAC calculations for a 38-mm-bore has been widely demonstrated. Nevertheless, an empirical EoS, such as that of Becker, Kistiakowsky and Wilson (BKW), is examined in this pressure range for different bore dimensions. Based on the appropriate choice of its adjustable parameters, it is applicable to a wide range of temperatures and pressures of combustion products that cover the whole field of gaseous to condensed explosives. The objective of this work is to improve the unsteady 1-D model as a useful tool to predict the thrust of the thermally choked ram accelerator propulsive mode by utilizing key results from the more computationally intensive 2-D or 3-D simulations. Velocity-distance calculations are in good agreement with experimental data from 25-mm, 30-mm, 38-mm, 90-mm, and 120-mm-bore experiments. Moreover the Thrust-Mach number calculations are performed and a good agreement with experimental data is also observed.