All-Speed Time-Accurate Underwater Projectile Calculations Using a Preconditioning Algorithm

An algorithm based on the combination of time-derivative preconditioning strategies with low-diffusion upwinding methods is developed and applied to multiphase, compressible flows characteristic of underwater projectile motion. Multiphase compressible flows are assumed to be in kinematic and thermodynamic equilibrium and are modeled using a homogeneous mixture formulation. Compressibility effects in liquid-phase water are modeled using a temperature-adjusted Tait equation, and gaseous phases (water vapor and air) are treated as an ideal gas. The algorithm is applied to subsonic and supersonic projectiles in water, general multiphase shock tubes, and a high-speed water entry problem. Low-speed solutions are presented and compared to experimental results for validation. Solutions for high-subsonic and transonic projectile flows are compared to experimental imaging results and theoretical results. Results are also presented for several multiphase shock tube calculations. Finally, calculations are presented for a high-speed axisymmetric supercavitating projectile during the important water entry phase of flight.