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

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. "A Hybrid Approach to Capture Free-Surface and Viscous Effects for a Ship in a Channel." Twenty-First Symposium on Naval Hydrodynamics. Washington, DC: The National Academies Press, 1997.

 Page 744

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Twenty-First Symposium on NAVAL HYDRODYNAMICS

We will present a combined numerical approach to capture most of these remaining effects. In a first step, a nonlinear Rankine source method will predict squat and trim for a ship in a channel. In a second step, a RANSE solver will use a grid for a ship fixed at the predicted squat and trim. The lateral extent of the grid will be considerably smaller than the actual channel. The velocities at the lateral boundary of the RANSE computational domain will be determined by the Rankine source code. However, the free-surface elevation will still be neglected assuming a flat undisturbed surface instead.

Computational Procedure

The flow is assumed to be symmetrical with respect to the hull center plane coinciding with the center plane of the channel. The problem is solved in two steps. In the first step, the inviscid free-surface flow in the channel is computed by a Rankine singularity method (RSM). Linear source panels are distributed above a finite section of the free surface. The panels are numerically evaluated by approximating them by a four-point source cluster, [24]. On the hull and the channel side wall, higher-order panels (parabolic in shape, linear in strength) are distributed. Mirror images of the sources at the channel bottom enforce that no water flows through the channel bottom. The nonlinear free-surface boundary condition is met in an iterative scheme that linearizes differences from arbitrary approximations of the potential and the wave elevation, Fig.1, [12]. The radiation and open-boundary conditions are enforced by shifting sources versus collocation points on the free surface. [25] gives more details on the method.

We describe now the automatic grid generation for the free-surface grid. The base 'wave length' is taken as The upstream end of the grid is 1.5 · max(0.4Lpp,λ) before FP for shallow water. (For infinite water, the factor is 1.0 instead of 1.5). The downstream end of the grid is max(0.6Lpp,λ) behind AP. The outer boundary in transverse direction BG is 0.35 of the grid length for unlimited flow, but taken at the channel wall (0.8L in our case) for a ship in a channel. The intended number of panels per wave length is 10. The intended number of panels in transverse direction is (BG–Δx)/(1.5Δx)+1, where Δx is the grid spacing in longitudinal direction. However, if the intended number of free-surface panels plus the number of hull panels exceeds 2500, the grid spacing in x- and y-direction is increased by the same factor until this condition is met. The innermost row of panels uses square panels, the rest of the panels is rectangular with a side ratio (Δyx) of approximately 1.5. The panels follow a 'grid waterline'. This is the upper rim of the discretized ship (1.5m above CWL in our case) which is modified towards the ends to enforce entrance angles of less than 31°. The channel wall grid follows the free-surface grid in longitudinal direction. In vertical direction the number of panels is the next integer to (h–Δx)/(2Δx)+1, but at least two. The uppermost row uses square panels. The free-surface panels are desingularized by a distance of Δx.

Fig. 1: Flow chart of iterative solution

In a second step, the viscous flow around the ship is solved. The ship is assumed fixed at the squat calculated in the first step. The deformation of the water surface is neglected and the water surface substituted by a flat symmetry plane. The computational domain does not extend in lateral direction to the channel walls. Instead, the inviscid velocities of the first step are taken as boundary condition on the lateral boundary. The RANSE solver is based on Kodama's method, [26]. It solves the continuity equation including a pseudo-compressibility term and the three momentum equations for incompressible turbu-

 Page 744
 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)