Investigation into the wave system of a generic submarine moving along a straight path beneath the free surface

Abstract

Abstract The present study aims to investigate the wave system of a generic submarine traveling along a straight path beneath the free surface by using the unsteady Reynolds-averaged Navier–Stokes equations with a Reynolds stress turbulence model implemented in commercial code STARCCM+ over submergence depths and body length Froude numbers ranging from h = 1 . 1 × D to h = 3 . 3 × D ( D : submarine diameter) and from F n = 0 . 205 to F n = 0 . 512 , respectively. The wave characteristics that are analyzed include the maximum wave height, wake angle and the centerline wave profiles at hump and hollow Froude numbers. The analysis of the centerline wave profiles at hump and hollow Froude numbers indicates that the interaction between the positive bow and the negative aft shoulder waves has a dominant effect on the submarine-generated wave system. Additionally, it is observed that an increase in Froude number or a decrease in submergence depth generally leads to an approximately consistent reduction in the wake angle. In this regard, to explain this reduction in the wake angle, an attempt is made to use an existing theoretical model, which estimates the ray angles along which the largest waves are located because of constructive interference between the positive bow and negative aft shoulder waves. Generally, a poor agreement is observed between the numerical wake angles and the theoretical ray angles. In spite of this poor agreement, the constructive interference effects between the positive bow wave and the negative aft shoulder wave is assumed to be the primary reason for the decrease in the wake angle with an increase in Froude number or a decrease in submergence depth. Moreover, the large discrepancies between the numerical wake angles and the theoretical ray angles suggest that to use the theoretical model for submarines, this model should be modified to account for the submergence depth effect on both the aft shoulder wave and the normalized distance between the origins of the main contributors to the submarine wave system.