Session: 06-05-04 Marine Hydrodynamics IV

Paper Number: 80485

80485 - On the Effect of Free-Surface Linearization on the Predicted Hydrodynamic Response of Underwater Vehicles Travelling Near the Free-Surface 

Control-oriented motion modeling supports the design of model-based control laws and state and disturbance estimators for shallow submerged vessels maneuvering in waves. The Lagrangian nonlinear maneuvering and seakeeping (LNMS) model [1] was developed from first principles to capture near-surface phenomena that are absent in more simplistic, deep water models but with a model structure that supports energy-based nonlinear control design. The LNMS model was reformulated and extended [2] so that model parameters could be directly computed from potential functions obtained using a high-order (geometry and source distribution) time-domain boundary element method (BEM). BEMs typically rely on model simplifications including potential flow assumptions and linearized free-surface boundary conditions. Such conditions apply linearized versions of the dynamic and kinematic boundary conditions at the calm water surface, valid for an assumption of small wave height and slope, and introduce increasing error as submergence decreases and/ or speed increases. Some nonlinear effects can be reintroduced into the model by incorporating nonlinear terms into the boundary conditions as well as imposing the conditions at the true free-surface interface through iterative free-surface deformation. Differences between the linear and nonlinear methods were studied in [3] and significant variance was observed in the hydrodynamic force and moment response for a body travelling with steady speed close to the free-surface. In order to better characterize the possible errors introduced into the LNMS model through state-dependent parameter computation using a BEM, a study of linear and nonlinear wave effects on a shallow submerged body is performed over a large Froude number and submergence range. A comparison of visual wave pattern, hydrodynamic force, and wave energy spectra is made between the linear version of the BEM and high fidelity CFD simulations. The CFD model considers an inviscid, free-surface flow solved by an unsteady second order accurate (time and space) finite volume Navier-Stokes solver. A volume fraction technique with sharp-interface free-surface capturing allows for a naturally occurring nonlinear, multiphase solution (except for approximations in the interface-capturing model) since no boundary conditions have to be applied at the free-surface.

Simulations are run for a 6:1 prolate spheroid travelling with steady forward velocity near a free-surface. The speeds range from FN=0.2-0.9 while the depths vary from 0.51 diameters to 4 diameters measured from the calm water surface to the body axis. Preliminary analysis of the two simulation methods reveal that using the nonlinear surface capturing approach results in approximately 20% larger wave resistance values compared to the linear BEM for a shallow submergence. These larger values correspond to larger wave heights and steeper wave slopes. Furthermore, the difference between the two methods decrease as either depth increases or speed decreases supporting the idea that the difference is explained by the linearized free-surface approximation.

Further comparisons will be made using a wave energy spectrum gathered from cuts of the free wave pattern. The spectral analysis allows for a higher level of quantitative comparison between the different cases, establishing a direct relation between the change in hydrodynamic forces and the energy content variation of the wave components, rather than a mere visual comparison of wave profile and force plots. In addition to the comparison between the panel method and inviscid CFD solutions, viscous simulations will also be performed to study the effects of viscosity and how to best incorporate those within the parameter-based LNMS model.

 [1] T. A. Battista, “Lagrangian Mechanics Modeling of Free Surface-Affected Marine Craft,”   Thesis, Virginia Polytechnic Institute and State University, Apr. 2018.

[2] S. Y. Jung, “Determining Parameters for a Lagrangian Mechanical System Model of a Submerged Vessel Maneuvering in Waves,” Thesis, Virginia Polytechnic Institute and State University, Mar.2020.

[3] W. Lambert and S. Brizzolara, “On the Effect of Non-Linear Boundary Conditions on the Wave Disturbance and Hydrodynamic Forces of Underwater Vehicles Travelling Near the Free-Surface,” American Society of Mechanical Engineers Digital Collection, Dec. 2020

Presenting Author: William Lambert Virginia Polytechnic Institute and State University

Authors:

William Lambert Virginia Polytechnic Institute and State University
Stefano Brizzolara Virginia Polytechnic Institute and State University
Craig Woolsey Virginia Polytechnic and State University