Numerical Methods for Seakeeping Problems

✍ Scribed by Bettar Ould el Moctar, Thomas E. Schellin, Heinrich Söding

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 292
• Category: Library

✦ Synopsis

The book describes currently applied and newly developed advanced numerical methods for wave-induced ship motions and loads. Besides well-established computational methods based on strip theory, panel methods and finite volume methods for unsteady Reynolds-averaged Navier-Stokes equations (URANS), recent advances like a fully nonlinear Rankine panel method, URANS calculations including elastic hull deformations, and an improved method to predict added resistance in waves are explained in detail. Furthermore, statistical methods to assess extreme motions and loads are described both for linear and nonlinear responses in a stationary seaway as well as during long-term ship operations. Results of motions and loads, computed using the various methods, are compared with each other and with results of model experiments.
Introductory chapters on fluid dynamics, motions of rigid and elastic ship hulls, numerical methods to compute fluid flows associated withwind waves, and the development and simulation of seaways complement the volume. The book will be of interest to post-graduate students, PhD candidates, as well as engineers in the field of naval architecture, ocean, and marine engineering.

✦ Table of Contents

Preface
Contents
1 Introduction
Reference
2 Fundamental Governing Equations
2.1 Governing Equations of Fluid Flow
2.1.1 Conservation Principles
2.1.2 Mass Conservation (Continuity Equation)
2.1.3 Momentum Conservation (Navier-Stokes Equation)
2.1.4 Flow of Incompressible Fluids
2.1.5 Potential Flow
2.2 Rigid Body Motions
2.2.1 Coordinate Systems
2.2.2 Kinematics
2.2.3 Motion Equations
2.2.4 Linearized Equations of Motion
Reference
3 Numerical Methods to Compute Incompressible Potential Flows
3.1 Source-Sink Method
3.2 Example: Two-Dimensional Flow Around Smooth Body Without Lift
3.3 Demonstration Program
3.4 Program Test
3.5 Arrangement of Source Points
3.6 Alternative Singularities
3.7 Symmetry; Mirror Principle
3.8 Steady Two-Dimensional Flow Around a Foil; Patch Method
Reference
4 Water Waves
4.1 Regular Waves
4.1.1 Airy Potential
4.1.2 Dispersion Relation
4.1.3 Corollaries
4.1.4 Stokes Waves
4.1.5 Linear Regular Waves in Deep and Shallow Water
4.1.6 Nonlinear Regular Waves in Deep and Shallow Water
4.2 Natural (Irregular) Waves
4.2.1 Linear Superposition
4.2.2 Nonlinear Natural Seaway
4.2.3 Wave Spectrum
4.2.4 Relations Between Wind and Seaway
4.2.5 Simulation of Natural Seaways
4.2.6 Statistics of Seaway Parameters
4.3 Appendix A: Fortan90 Program for Testing Formula (4.41)
References
5 Strip Methods
5.1 History
5.2 Computing Added Mass, Damping, and Excitation in Two-Dimensional Flow
5.2.1 Fundamental Equations
5.2.2 Preparation of the Flow Potential
5.2.3 Numerical Method
5.2.4 Determination of Pressure, Force, and Moment
5.2.5 Verification
5.3 Determination of Ship Motions in a Regular Wave
5.3.1 Coordinate Systems
5.3.2 Equation of Motion
5.3.3 Restoring Forces
5.3.4 Radiation Forces
5.3.5 Exciting Force
5.3.6 Application
5.4 Hull Interaction in Multi-hull Vessels
5.4.1 Hull Interaction Caused by Radiation Waves
5.4.2 Hull Interaction Caused by Diffraction Waves
5.4.3 Validation
References
6 Green Function Methods
6.1 Introduction
6.2 The Encounter Frequency Panel Method
6.3 Determination of Radiation and Diffraction Potentials
6.4 Pressure Force and Moment
6.5 Determination of Ship Motions
6.6 Nonlinear Pressure Correction
References
7 Linear Rankine Source Methods
7.1 Introduction
7.2 Rankine Source Method for the Stationary Flow Around a Ship with Forward Speed
7.2.1 Basic Boundary Value Problem
7.2.2 Wave Breaking
7.2.3 Representation of the Disturbance Potential by Source Potentials
7.2.4 Patch Method and Body Boundary Condition
7.2.5 Numerical Treatment of Free-Surface Conditions
7.2.6 Solution of the Equation System
7.2.7 Further Computations
7.3 Rankine Source Method for the Time-Harmonic Flow
7.3.1 Superposition of Potentials
7.3.2 Body Boundary Condition
7.3.3 Dynamic Free-Surface Boundary Condition
7.3.4 Kinematic Free-Surface Boundary Condition
7.3.5 Numerical Treatment of Free-Surface Conditions
7.3.6 Boundary Condition at a Transom
7.3.7 Other Conditions
7.3.8 Free-Surface Panel Grid
7.3.9 Solving the Equation System
7.3.10 Calculation of Hull Pressure
7.3.11 Pressure Force and Moment
7.3.12 Motion Equation
References
8 Nonlinear Rankine Panel Methods
8.1 Introduction
8.2 Coordinate Systems
8.3 Subdivision of the Flow Potential
8.4 Panel Meshes and Time Derivatives
8.5 Body Boundary Conditions
8.6 Free-Surface Boundary Conditions
8.7 Transom Condition
8.8 Radiation Condition
8.9 Numerical Method to Satisfy the Body Boundary Condition
8.10 Numerical Method to Satisfy the Free Surface Boundary Conditions
8.11 Determination of Source Strengths
8.12 Determination of Body Force and Moment
8.13 Motion Equations
8.14 Verification
References
9 Viscous Field Methods
9.1 Introduction
9.2 Reynolds-Averaged Navier-Stokes Equations
9.3 Large Eddy Simulation and Hybrid Models
9.4 Discretization
9.4.1 Approximation of Area and Volume Integrals
9.4.2 Convective Fluxes
9.4.3 Diffusive Fluxes
9.4.4 Computation of Source Terms
9.4.5 Time Marching Methods
9.5 Moving Grids
9.6 Algebraic System of Equations
9.6.1 Under-Relaxation
9.7 Initial Values and Boundary Conditions
9.7.1 Wall Functions
9.8 Pressure-Velocity Coupling
9.9 Numerical Grids
9.10 Free-Surface Flows
9.10.1 Front-Tracking Methods
9.10.2 Front-Capturing Methods
9.11 Coupling Flow Equations and Rigid Body Motion Equations
9.12 Wave Generation and Damping in Field Methods
9.12.1 Preliminaries
9.12.2 An Intuitive Approach
9.12.3 Forcing Zones
9.12.4 Simulation Setup
9.12.5 Space and Time Discretization
9.13 Numerical Errors
9.13.1 Discretization Errors
9.13.2 Modeling Errors
9.13.3 Iteration Errors
9.13.4 Reference Procedures to Determine Discretization Errors and Uncertainties
9.14 Application
9.14.1 Test Case Description
9.14.2 Results
References
10 Wave-Induced Hull Vibrations
10.1 Overview
10.2 Modeling Stiffness and Mass
10.2.1 Finite-Element Discretization
10.2.2 Use of Approximate Modes
10.2.3 Mass and Stiffness Matrix
10.2.4 Other Contributions
10.3 Vibration Damping
10.3.1 Transom Damping
10.3.2 Wave Radiation Damping
10.3.3 Other Causes of Damping
10.3.4 Results
10.4 Comparison Between Computed and Measured Loads
References
11 Additional Forces and Moments
11.1 Weight
11.2 Roll Restoring Moment
11.3 Additional Roll Damping
11.4 Additional Surge Damping
11.5 Fins
11.5.1 Preliminaries
11.5.2 Force Due to Accelerations
11.5.3 Force Due to Velocity and Angle of Attack
11.5.4 Effect of Inflow Conditions
11.5.5 Influence of Oscillation Frequency
11.5.6 Special Cases
11.6 Foil Effect of the Hull
11.7 Bilge Keels
11.8 Control Forces
References
12 Special Topics
12.1 Sails
12.2 Suspended Load
12.3 Roll Damping Tanks
12.4 Negative Encounter Frequency
12.5 Long Encounter Periods and Surf-Riding
12.6 Motion Restraints
Reference
13 Further Transfer Functions
13.1 Hull Pressure
13.2 Absolute and Relative Motions at Body-Fixed Points
13.3 Force and Moment at Transverse Cross Sections
13.4 Water Motion in a Moonpool
Reference
14 Drift Force and Added Resistance
14.1 Preliminaries
14.2 Drift Force Due to Pressure Acting on the Surface up to the Mean Waterline
14.3 Drift Force Due to Pressure Acting Between the Average and the Actual Waterline
14.4 Verification
14.5 Appendix: Determination of the Hesse Matrix of Potentials
References
15 Comparison Study
15.1 Description of Test Case
15.2 Computational Methods
15.3 Results
References
16 Ships in Natural Seaways
16.1 Statistics of Linear Responses in a Stationary Seaway
16.2 Statistics of Nonlinear Responses in a Stationary Seaway
16.2.1 Nonlinear Function of a Linear Response
16.2.2 Function of Several Linear Responses
16.2.3 Other Nonlinear Responses
16.3 Long-Term Distribution of Responses
References
17 Miscellaneous Topics
17.1 Simulating Nonlinear Roll Motions
17.2 Simulating Damaged Ships in a Seaway
17.3 Simulating Planing Boats
17.4 Perturbators
17.4.1 One-Frequency Second-Order Perturbators
17.4.2 Two-Frequency Second-Order Perturbators
17.5 Seakeeping of Catamarans and Weinblums
References
471933_1_En_18_Chapter_OnlinePDF.pdf
18 Correction to: Water Waves
Correction to: Chapter 4 in: B. O. el Moctar et al., Numerical Methods for Seakeeping Problems, https://doi.org/10.1007/978-3-030-62561-0_4