Improved One-Dimensional Unsteady Modeling of Thermally Choked Ram Accelerator in Subdetonative Velocity Regime

The subdetonative propulsion mode using thermal choking has been studied with a one-dimensional (1D) real gas model that included projectile acceleration. Numerical results from a control volume analysis that accounted for unsteady flow effects established that the thrust coefficient versus Mach number profile was lower than that obtained with a quasi-steady model. This deviation correlates with experimental results obtained in a 38-mm-bore ram accelerator at 5.15 MPa fill pressure. Theoretical calculations were initially carried out with the assumption that the combustion process thermally choked the flow about one projectile length behind the projectile base. Thus the control volume length used in this 1D modeling was twice the projectile length, which is consistent with experimental observations at velocities corresponding to Mach number less than 3.5. Yet the choice of the length of the combustion zone and thus the control volume length remains a key issue in the unsteady modeling of the ram accelerator. The present paper provides a refinement of the unsteady one-dimensional model in which the effect of control volume length on the thrust coefficient and the projectile acceleration were investigated. For this purpose the control volume length determined from computational fluid dynamics (CFD) as a function of projectile Mach number was applied. The CFD modeling utilized the Reynolds-averaged Navier-Stokes (RANS) equations to numerically simulate the reacting flow in the ram accelerator. The shear-stress transport turbulence and the eddy dissipation combustion models were used along with a detailed chemical kinetic mechanism with six species and five-step reactions to account for the influence of turbulence and rate of heat release on the length of the combustion zone. These CFD computational results provided Mach number dependent estimates for the control volume length that were implemented in the 1D modeling. Results from the proposed improved 1D unsteady modeling were compared and validated with ram accelerator experimental data with significant improvements in terms of the predicted thrust dependence on Mach number.