Effects of pitch angle on a near free surface underwater vehicle

Simulations of an underwater vehicle were conducted to investigate the effects of steady pitch angle, Froude number, and submergence depth. A shallow submerged (D* = 1.1) to a deeply submerged (D* = 6.6) SUBOFF was investigated over a range of steady pitch angles and Froude numbers. Results show that proximity to the free surface causes increased resistance, heave and pitch moment and that free surface effects diminish rapidly with increased submergence depth. Even though D* = 3.3 is typically quoted as being the deeply submerged threshold, free surface effects can still be observed especially at large pitch angles. At pitch angle, asymmetry can be seen between the pressure distribution of the upper and lower surfaces of the SUBOFF, with a phase shift of the hydrodynamic forces and moments. At smaller pitch angles, the changes in hydrodynamic forces and moments stay relatively linear at an offset from zero degrees. At larger pitch angles, the hydrodynamic forces and moments become non-linear due to crossflow separation and air entrainment over the bow/stern. Additionally, the potential of the stern planes to cope with free surface effects were investigated, showing the safety threshold with respect to Froude number, submergence depth, and hull pitch angle.