On the Effect of Non-Linear Boundary Conditions on the Wave Disturbance and Hydrodynamic Forces of Underwater Vehicles Travelling Near the Free-Surface

Abstract

This study compares the effect of non-linear free-surface boundary conditions for a high-order non-linear free-surface Rankine-source boundary element method on wave disturbance and hydrodynamic forces acting on an underwater vehicle travelling near a calm free-surface. In particular, simulations for a steady nonaxisymmetric prolate spheroid using different basis flows and linearization techniques were compared to an analytical method achieved by Chatjigeorgiou using a multipole expansion of Green’s functions. It appears that at low Froude numbers, the basis flow used in the formulation contributes significantly to differences in the steady solutions for wave resistance and pitch, whereas for higher Froude numbers the linearization technique becomes a more defining feature. Upon observation of the analytical solution for wave resistance, one can see that it was formed under a Neumann-Kelvin formulation and this is supported by the Neumann-Kelvin simulations converging well to the analytical solution. Further comparisons were made using a wave directional energy spectrum gathered from transverse wave cuts of the free wave pattern. The spectral analysis allows for a higher level of comparison between all of the different cases, establishing a direct relation between the change in wave resistance and the energy content variation of the particular wave spectrum components.

The Effect of a Linear Free Surface Boundary Condition on the Steady-State Wave-Making of Shallowly Submerged Underwater Vehicles

“…Very few experimental results are available for reasonable comparison to the BEM, and another numerical solution is therefore explored. A short investigation showed that the nonlinear settings for the BEM used by Lambert and Brizzolara [14] are inconsistent with respect to depth; therefore, a Reynolds-Averaged Navier-Stokes Equations (RANSE) solver with the volume of fluid free-surface capturing is used. This simulation method is applied using an inviscid fluid so that conditions similar to potential flow can be achieved.…”

“…A transverse wave cut method [29] is applied to estimate the wave-making characteristics in each simulated case using the longitudinal wave slope along a perpendicular slice to the wave pattern located 0.6 body lengths (1.2 m) behind the stern. The transverse wave cut method has previously been used to identify nonlinearities in the wave patterns produced by the linear and nonlinear versions of the boundary element method used throughout this study [14]. This method has also been successfully applied to characterize the wave-making properties of high speed craft [30] and validated against other wave-cut methods [31].…”

“…Lambert and Brizzolara [14] present a study exploring the effect of incorporating nonlinear free surface effects within the BEM originally used for parameter computations within the LNMS model. Higher-order terms within the free-surface boundary conditions were retained while also updating the free surface through an iterative process so that the conditions could be applied at the true free-surface elevation.…”

“…In an effort to better characterize the effects of making linear free-surface assumptions and further the work completed by Lambert and Brizzolara [14], a study comparing the hydrodynamic responses of a vehicle traveling beneath a free surface modeled with different theoretical formulations is presented here. While nonlinear free-surface effects have been widely investigated with boundary-element methods for surface-piercing vessels, the need for sufficient characterization of the errors associated with applying linear free-surface boundary conditions is emphasized in cases where the surface remains unbroken by a submerged body.…”

Hydrodynamic Behavior of a Submerged Spheroid in Close Proximity to the Sea Surface

“…Submarines frequently descend to periscope or snorkeling depths, for target exploration or ba ery recharging, wherein they encounter environmental loads, including waves, currents, resistance and suction forces [23,24]. Numerous studies have investigated the impact of the free water surface on underwater vehicles using both numerical and experimental methods [25][26][27][28][29][30][31][32][33][34][35]. Given the imposed forces experienced by submerged structures in different water depths, submarines must maintain specific navigational poses (depth, roll and trim angle), necessitating extensive research on depth control strategies.…”