A Very Simple Model for the Wake Hollow Behind a High-Speed Displacement Hull

Naval architects involved in the design of high-speed displacement hulls often need to model the wake hollow or transom cavity that is generated by these hulls. This model is then used to estimate such effects as the virtual length increase of the hull or other parameters of interest.The problem is that modeling of the wake hollow has heretofore only been possible by high-fidelity methods of computational fluid dynamics, which require setup efforts and software investments that may not be reasonable for all projects.This paper is based on the published work of Vorus (2009), in which he developed a mathematical theory for the downstream wake closure characteristics of fully ventilated wakes of high-speed ships with transom sterns. The theory uses the linear thin body approximations with gravity in a formulation consistent with thin body theory of wave resistance. The authors subject this theory to a numerical analysis to develop a simple formula for calculating the length of the wake. The authors then develop a Very Simple Model (VSM) based on the basic dynamics of the projectile motion of a particle (i.e., a fluid particle). This simple formula for wake hollow developed from the numerical analysis of Vorus’ theory is exactly that which is used in the development of the ballistic model.The authors have found a VSM of the wake hollow that produces surprisingly good accord with higher fidelity models and the linear potential theory of Vorus, and yet is a simple algebraic formula. We offer this VSM of the wake hollow either as the full model for a simple project, or as the starting “seed geometry” for CFD solution, to eliminate the number of iterations required.…#169;