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## Twenty-First Symposium on Naval Hydrodynamics (1997) Commission on Physical Sciences, Mathematics, and Applications (CPSMA)

### Citation Manager

. "Time-Domain Calculations of First-and Second-Order Forces on a Vessel Sailing in Waves." Twenty-First Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press, 1997.

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 Page 178

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Twenty-First Symposium on NAVAL HYDRODYNAMICS

were satisfactory. We have extended this method with, among other things, a frequency independent absorbing boundary condition [8].

In this paper we apply the method to a LNG carrier at service speed. The forward speed of the commercial tanker considered up to now is very low, the maximum Froude number is 0.018, i.e. 2 knots, while the usual speed of a 125,000m3 LNG carrier is about 20 knots (i.e. Froude number is 0.2). This fact causes some problems in our algorithm. We study increasing speed and the effect on our absorbing boundary condition. To remove the instabilities on the free-surface due to increasing forward speed, we introduce upwind discretization. Both cases were done in the two-and tree-dimensional algorithm.

In the first section we give the main idea of the Prins' algorithm and our extension to a frequency independent boundary condition. In the second section we study increasing speed and the the effect on our algorithm. In the third section results are presented for a 125,000m3 LNG carrier, at deep water. We will calculate the drift force or added resistance not only for low forward speed, but also the added resistance for higher forward speed has been studied. In order to check the method, we compare our results with measurements of Wichers [11] and with strip theory results [1, 2]. The last section we give the conclusions and ideas for further research.

##### Time-domain algorithm

The time-domain algorithm given below is based on the one given by Prins [7].

The physical fluid domain is an infinite (or large) domain. The computational domain cannot be infinite, so we have to introduce artificial boundaries and proper boundary conditions. In the literature several methods have been proposed to absorb free surface waves. On the basis of a literature search, Prins decided to use an extension of the Sommerfeld radiation condition for two families of waves. The disadvantage of this Sommerfeld condition is that it is dependent on the wave frequency, so it cannot handle non-harmonic waves, and on the forward velocity.

Keller and Givoli [3] introduce a semi-discrete DtN-method, using an artificial boundary, dividing the original domain into a computational and a residual domain (the interior and exterior). In our method we use a three-dimensional boundary condition independent of the wave frequency, using the idea of the Givoli's method with Prins' algorithm. In the interior domain we use the same mathematical model as Prins [7] use but we do not implement a Sommerfeld radiation condition on the artificial boundary.

###### The interior problem

We consider a vessel sailing with an uniform velocity U in the negative x-direction, or an uniform current with velocity U is directed in the positive x-direction. Regular waves are travelling in the water-surface in a direction which makes an angel β with the positive x-direction, see figure 1. The coordinate system is chosen such that the undisturbed free surface coincides with the plane z=0 and the centre of the gravity of the hull is on the z-axis, with z pointing upwards. The hull is free to move in all directions and to rotate around the main axes.

FIGURE 1: The geometry

We assume the following restrictions: there is no viscosity, the fluid is incompressible and homogeneous, and the flow is irrotational. We introduce the velocity potential Φ, which has to satisfy the Laplace equation

(1)

By using the dynamic and kinematic conditions and splitting the potential into a steady and an unsteady part, like

we get the linearized free-surface condition on the undisturbed free surface

(2)

with subscripts denoting the partial derivative. In contrast with the two-dimensional algorithm, we do not include terms of Including them would cause us to calculate higher derivatives of the unsteady potential at the free surface. This would increase the computation time, because the need of the very fine mesh.

 Page 178
 Front Matter (R1-R16) Opening Remarks (1-4) Progress Toward Understanding How Waves Break (5-28) Radiation and Diffraction Waves of a Ship at Forward Speed (29-44) Nonlinear Ship Motions and Wave-Induced Loads by a Rankine Method (45-63) Nonlinear Water Wave Computations Using a Multipole Accelerated, Desingularized Method (64-74) Computations of Wave Loads Using a B-Spline Panel Method (75-92) Simulation of Strongly Nonlinear Wave Generation and Wave-Body Interactions Using a 3-D Model (93-109) Analysis of Interactions Between Nonlinear Waves and Bodies by Domain Decomposition (110-119) Fourier-Kochin Theory of Free-Surface Flows (120-135) 24-inch Water Tunnel Flow Field Measurements During Propeller Crashback (136-146) Accuracy of Wave Pattern Analysis Methods in Towing Tanks (147-160) Unsteady Three-Dimensional Cross-Flow Separation Measurements on a Prolate Spheroid Undergoing Time-Dependent Maneuvers (161-176) Time-Domain Calculations of First-and Second-Order Forces on a Vessel Sailing in Waves (177-188) Third-Order Volterra Modeling Ship Responses Based on Regular Wave Results (189-204) Nonlinearly Interacting Responses of the Two Rotational Modes of Motion-Roll and Pitch Motions (205-219) Nonlinear Shallow-Water Flow on Deck Coupled with Ship Motion (220-234) Radar Backscatter of a V-like Ship Wake from a Sea Surface Covered by Surfactants (235-248) Turbulent Free-Surface Flows: A Comparison Between Numerical Simulations and Experimental Measurements (249-265) Conductivity Measurements in the Wake of Submerged Bodies in Density-Stratified Media (266-277) Macro Wake Measurements for a Range of Ships (278-290) Time-Marching CFD Simulation for Moving Boundary Problems (291-311) Yaw Effects on Model-Scale Ship Flows (312-327) A Multigrid Velocity-Pressure-Free Surface Elevation Fully Coupled Solver for Calculation of Turbulent Incompressible Flow around a Hull (328-345) The Shoulder Wave and Separation Generated by a Surface-Piercing Strut (346-358) Vorticity Fields due to Rolling Bodies in a Free Surface-Experiment and Theory (359-376) Numerical Calculations of Ship Stern Flows at Full-Scale Reynolds Numbers (377-391) Near-and Far-Field CFD for a Naval Combatant Including Thermal-Stratification and Two-Fluid Modeling (392-407) Water Entry of Arbitrary Two-Dimensional Sections with and Without Flow Separation (408-423) Coupled Hydrodynamic Impact and Elastic Response (424-437) A Practical Prediction of Wave-Induced Structural Responses in Ships with Large Amplitude Motion (438-452) Evaluation of Eddy Viscosity and Second-Moment Turbulence Closures for Steady Flows Around Ships (453-469) On the Modeling of the Flow Past a Free-Surface-Piercing Flat Plate (470-477) Self-Propelled Maneuvering Underwater Vehicles (478-489) Spray Formation at the Free Surface of Turbulent Bow Sheets (490-505) Numerical Simulation of Three-Dimensional Breaking Waves About Ships (506-519) Generation Mechanisms and Sources of Vorticity Within a Spilling Breaking Wave (520-533) The Flow Field in Steady Breaking Waves (534-549) Freak Waves-A Three-Dimensional Wave Simulation (550-560) Bluff Body Hydrodynamics (561-579) Large-Eddy Simulation of the Vortical Motion Resulting from Flow over Bluff Bodies (580-591) The Wake of a Bluff Body Moving Through Waves (592-604) Low-Dimensional Modeling of Flow-Induced Vibrations via Proper Orthogonal Decomposition (605-621) Measurements of Hydrodynamic Damping of Bluff Bodies with Application to the Prediction of Viscous Damping of TLP Hulls (622-634) Hydrodynamics in Advanced Sailing Design (635-660) Divergent Bow Waves (661-679) A Method for the Optimization of Ship Hulls from a Resistance Point of View (680-696) Hydrodynamic Optimization of Fast-Displacement Catamarans (697-714) On Ships at Supercritical Speeds (715-726) The Influence of a Bottom Mud Layer on the Steady-State Hydrodynamics of Marine Vehicles (727-742) A Hybrid Approach to Capture Free-Surface and Viscous Effects for a Ship in a Channel (743-755) Shock Waves in Cloud Cavitation (756-771) Asymptotic Solution of the Flow Problem and Estimate of Delay of Cavitation Inception for a Hydrofoil with a Jet Flap (772-782) Examination of the Flow Near the Leading Edge and Closure of Stable Attached Cavitation (783-793) Numerical Investigation on the Turbulent and Vortical Flows Beneath the Free Surface Around Struts (794-811) Steep and Breaking Faraday Waves (812-826) The Forces Exerted by Internal Waves on a Restrained Body Submerged in a Stratified Fluid (827-838) Influence of the Cavitation Nuclei on the Cavitation Bucket when Predicting the Full-Scale Behavior of a Marine Propeller (839-850) Inception, Development, and Noise of a Tip Vortex Cavitation (851-864) Velocity and Turbulence in the Near-Field Region of Tip Vortices from Elliptical Wings: Its Impact on Cavitation (865-881) Calculations of Pressure Fluctuations on the Ship Hull Induced by Intermittently Cavitating Propellers (882-897) Hydroacoustic Considerations in Marine Propulsor Design (898-912) Prediction of Unsteady Performance of Marine Propellers with Cavitation Using Surface-Panel Method (913-929) A Comparitive Study of Conventional and Tip-Fin Propeller Performance (930-945) A New Way of Stimulating Whale Tail Propulsion (946-958) Effects of Tip-Clearance Flows (959-972) Experiments in the Swirling Wake of a Self-Propelled Axisymmetric Body (973-985) Hydrodynamic Forces on a Surface-Piercing Plate in Steady Maneuvering Motion (986-996) Advances in Panel Methods (997-1006) Effect of Ship Motion on DD-963 Ship Airwake Simulated by Multizone Navier-Stokes Solution (1007-1017) Large-Eddy Simulation of Decaying Free-Surface Turbulence with Dynamic Mixed Subgrid-Scale Models (1018-1032) Fully Nonlinear Hydrodynamic Calculations for Ship Design on Parallel Computing Platforms (1033-1047) Validation of Incompressible Flow Computation of Forces and Moments on Axisymmetric Bodies Undergoing Constant Radius Turning (1048-1060) The Validation of CFD Predictions of Nominal Wake for the SUBOFF Fully Appended Geometry (1061-1076) Appendix-List of Participants (1077-1084)