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

An algorithm based on the combination of time-derivativepreconditioning strategies with low-diffusion upwinding methods is developed and applied to multiphase, compressible flowscharacteristic of underwater projectile motion. Multiphase compressible flowsare assumed to be in kinematic and thermodynamic equilibriumand 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 projectilesin 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 projectileflows are compared to experimental imaging results and theoretical results. Results are also presented for several multiphase shock tubecalculations. Finally, calculations are presented for a high-speed axisymmetric supercavitating projectileduring the important water entry phase of flight.