h Star Manual

HYDROSTAR FOR EXPERTS

USER MANUAL

March 2011

This document has been prepared for the users of HydroStar for version 6.1 and above anddeals with the aspects related to the computation of first and second order loads and motionsfor arbitrary bodies in deep and finite depth waters, with or without forward speed.

Research DepartmentBUREAU VERITAS

92571 Neuilly-Sur-SeineTel: +33 (0)1 55 24 70 00Fax: +33 (0)1 55 24 70 26

HydroStar For Experts BV (1991-2011) is distributed by Bureau Veritas.

First Printing, April 2006Revised, August 2007Revised, September 2007Revised, April 2008Revised, October 2008Revised, December 2008Revised, March 2009Revised, May 2010Revised, March 2011

cBureau Veritas

Contacts:

Bureau Veritas FranceDr. Xiao-bo CHENe-mail: [email protected]

Guillaume de-HAUTECLOCQUEe-mail: [email protected]

Bureau Veritas ChinaBrice Le-GALLOe-mail: [email protected]

Haixia Xue-mail: [email protected]

Cong YUe-mail: [email protected]

Bureau Veritas KoreaYun-Suk CHUNGe-mail: [email protected]

Bureau Veritas USAPaulo BIASOTTOe-mail: [email protected]

Bureau Veritas BrazilFlavia REZENDEe-mail: [email protected]

Hydrostar User Manual

Release Notes

Version 6.0:

Correction of bug in hsrdf for finite water depth and when no symmetry condition wasused (example, multi-body in finite water depth).

Inclusion of sidewall effects in hsrdf (page 5-6). Construction of transfer function of relative motions between two bodies in hsrao (page

12-12).

Construction of QTFs according to O() approximation in hsrao (pages 10-8,12-15) Correction of bug in hsmec on the hydrostatic stiffness for the applications with tanks Modification of hsmec for the applications with tanks: the global mechanical properties

including the liquid in tanks must be given (page 6-4).

Modification of the limit on the number of characters of the input files. The name of theinput files was limited in the previous versions to 15 characters and has been extended to80 characters

Modification of the limit on the number of characters of the FILENAME used in the inputfile of hsrdf and hsmec . In the previous versions the limit was 3 characters. It has beenextended to 15 characters.

Construction of input files for Ariane v7 in hsrao (page 12-17). Modification of hsrsn . Not only the resonance frequencies are displayed in the screen,

but also the Eigen vectors associates to each resonant mode.

Use of LU decomposition for the solution of the linear system instead of Gauss Elim-ination.

Modification of computation progress display in hsrsn . The computation time for eachfrequency as well as the remaining computation time are displayed in the screen.


Version 6.10:

More efficient compilation. Calculation about 40% faster. Middle-Field implementation improved in hsqtf , the control surface can now coincide

with the free surface, this leads to better convergence

Automatic control surface generation improved (Multi-body, more parameters) Manual updated (phase convention error corrected and more details about the 2nd order

calculations)

Modification in output for Ariane7 (Added mass format changed) in hsrao Spectral tool StarSpec v1.10 included. hspec and hslps are available in HydroStar console.

For further information, refer to StarSpec user guide.

Version 6.11:

Install (improved) : Restart not needed anymore HSlec (bug fixed) : Automatic free-surface generation in some multi-body cases fixed HSchk (bug fixed) : Visualisation of sections for bodies with very low draft HSmcn (bug fixed) : Recombinaison of several HStnk calculations fixed HSmcn (new) : Calculation of multi-body cases with internal tanks (in only one body) HSmcn (improved) : Beam damping model linearisation improved for better convergence HSmcn (bug fixed) : NOTANKS option fixed HSqtf (bug fixed) : Number of heading in HSqtf calculation not limited to 50 anymore HSrao (bug fixed) : Ariane7 output when HSdft is not run works HSrao (new) : Wave reference point written in Ariane7 output HSrao (new) : Orcaflex output HSpec (new) : Long-term extrem assiocated to a probability in a reference duration HSpec (new) : Short-term extrem assiocated to a probability in a sea-state duration HSpec (new) : Spline interpolation of RAOs HSpec (new) : Wrapped normal spreading HSwav (bug fixed) : Crash with some meshes, fixed

Version 6.20:

HSpec (bug fixed) : Problem with m2 calculation when using both speed and spreadingfixed

HSpln (new) : New module to interpolate through HSrdf results HSrdf (new) : Iterative solver as an option (Keywords : SOLMETHOD GMRES) HSbln (new) : New module to equilibrate a ship on still water HSdft (new) : Side wall effect option HSqtf (bug fixed) : Correction of vertical 2nd order loads (Affected only moments Mx

and My with Near-Field formulation.)

Contents

Release Notes

Introduction 01

1 Getting Started 111.1 Hardware configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.2 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3 HydroStar interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4 Running tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Overview 212.1 HydroStar structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2 Conventions used in HydroStar . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3 Units used in HydroStar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Mesh Generation 313.1 Single simple geometry mesh generation . . . . . . . . . . . . . . . . . . . . . . 313.2 Bodies composed by various simple geometries . . . . . . . . . . . . . . . . . . . 35

3.2.1 Example of Input file for hsmsh . . . . . . . . . . . . . . . . . . . . . . . 3103.2.2 Generating the mesh using hsmsh . . . . . . . . . . . . . . . . . . . . . . 310

3.3 Use AMG to generate Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3113.4 Mesh equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

4 Reading the Mesh 414.1 Input file format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.2 Input file for a single body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.3 Input file for multi bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.4 Input file including dissipation zone . . . . . . . . . . . . . . . . . . . . . . . . . 494.5 Input file including tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4134.6 Input file of hybrid model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416


4.7 Reading the input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4174.8 Getting information about the mesh . . . . . . . . . . . . . . . . . . . . . . . . . 4194.9 Preliminary verificaton of the mesh . . . . . . . . . . . . . . . . . . . . . . . . . 4204.10 Checking the hydrostatic properties . . . . . . . . . . . . . . . . . . . . . . . . . 4214.11 Visualization of the mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

5 Diffraction radiation computation 515.1 Input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.2 Elimination of irregular frequencies . . . . . . . . . . . . . . . . . . . . . . . . . 555.3 Encounter frequency approximation . . . . . . . . . . . . . . . . . . . . . . . . . 565.4 Sidewall Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.5 Diffraction and radiation computation . . . . . . . . . . . . . . . . . . . . . . . 575.6 Radiation/Diffraction interpolation : HSpln module . . . . . . . . . . . . . . . . 575.7 Radiation computation inside tanks . . . . . . . . . . . . . . . . . . . . . . . . . 58

6 Motion Computation 616.1 Input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.2 Input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.2.1 Centre of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.2.2 Gyration Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.2.3 Inertia Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.2.4 Stiffness Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.2.5 Damping Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.3 Computing the vessels motions . . . . . . . . . . . . . . . . . . . . . . . . . . . 610

7 Global wave efforts computation 717.1 Global wave loads for ships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717.2 Global wave loads for non slender bodies . . . . . . . . . . . . . . . . . . . . . . 74

8 Waves visualization 81

9 Pressure and wave elevation computation 91

10 Second order computation 10110.1 Mean drift loads in uni-directional waves . . . . . . . . . . . . . . . . . . . . . . 102

10.1.1 Input file for hsdft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10210.1.2 Checking and visualizing the control surface . . . . . . . . . . . . . . . . 10410.1.3 Running hsdft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

10.2 Mean drift loads in bi-directional waves . . . . . . . . . . . . . . . . . . . . . . . 105

10.2.1 Input file for hsmdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10510.2.2 Running hsmdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

10.3 Full QTF computation in uni- and bi-directional waves . . . . . . . . . . . . . . 10610.3.1 Input file for hsamg and hsqtf . . . . . . . . . . . . . . . . . . . . . . . . 10610.3.2 Running HydroStar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10710.3.3 O() Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

11 FEM model interface 11111.1 Input files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

11.1.1 FEM model input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11111.1.2 Input file with the pressure transfer information . . . . . . . . . . . . . . 114

11.2 Running hsfem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11611.2.1 Reading the pressures by NASTRAN . . . . . . . . . . . . . . . . . . . . 116

12 Construction of the transfer functions 12912.1 Input File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12912.2 Running hsrao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1218

A Examples A1A.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1A.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A15

B Index of commands B1

C VISU4D interface C1

D References D1

08 Hydrostar User Manual

Introduction

HydroStar is the hydrodynamic software developed in Bureau Veritas since 1991, that providesa complete solution of first order problem of wave diffraction and radiation and also the QTFof second order low-frequency wave loads for floating body with or without forward speed indeep water and in finite water depth.

For the versions 4.0 and above, the QTF (Quadratic Transfer Function) of second-order waveloading can be computed by using three different formulations: the new middle-field formula-tion plus the classical near-field formulation consisting of direct pressure integration and thefar-field formulation derived from the theorem of momentum conservation. In version 5.0 thenear-field and middle-field formulations have been extended to the case of cross waves not onlyfor the calculation of mean drift loads but also for the QTF of low-frequency loads. Addition-ally, the control surface needed when middle-field is used can be now automatically generatedby the program.

The following advanced fonctionalities are present in HydroStar :

Fairly perfect fluid formulation: In the classical potential theory theres no limitin predicting resonant wave kinematics while the resonant motion is in reality largelydamped by different mechanisms. In order to avoid unrealistic resonant wave motion, wehave added a fictitious force to the momentum equation in the same way as Guevel (1982)to represent the energy dissipation of various sources without modifying the inviscid andirrotational properties. As a result a dissipation term is present in the classical boundarycondition over the free surface. The formulation of the so-called fairly-perfect fluidis a sound-basis applicable for a number of analysis. One example of application is theprediction of wave kinematics in the gap between two vessels in side-by-side configuration.

Green function and influence coefficients: The integral equation of the first-orderboundary value problem is derived by making use of the Green theorem. The Greenfunction involved in the wave diffraction and radiation problem is then formulated as thefundamental solution expressed by the Fourier-Hankel integral. The finite depth Greenfunction is decomposed into the deepwater Green function and two regular functions rep-resenting the effect of the seabed. The regular functions are then evaluated accurately andapproximated by Chebychev polynomials of three variables. Furthermore, the involvedspecial functions and the deepwater Green function are also approximated by Chebychev

01


polynomials of one and two variables, respectively. It is shown that polynomial approxi-mations are extremely efficient in computation of the Green function. Furthermore, theoriginality and interesting features of the formulation of the Green function in water of fi-nite depth given in Chen (1993) lead us to develop our efficient algorithms of its numericalcomputation.

Removal of irregular frequencies: In the Boundary Integral Equation (BIE) wemake use of the Green function which satisfies the governing equation in the fluid domain.Thus, the real physical problem exterior to the body surface and the fictitious interiorproblem are solved at the same time. If the Green function is chosen in such way that theinterior problem has no unique solution at some eigen-frequencies, the exterior solutionwill be also affected and important numerical errors will arise around these frequencies.The method adopted to remove those irregular frequencies is the extension of the BIEto a fictitious free surface in the interior of the body, taking advantage of the fact thatwe can modify the boundary value problem in the interior domain in such way that ithas a unique solution. If we discretize the interior surface in an appropriate way, we mayeliminate all the irregular frequencies or at least shift them sufficiently far away. Theinterior surface mesh is automatically generated by HydroStar .

Seakeeping-sloshing coupled analysis: In HydroStar we consider the seakeeping andthe sloshing problems separately. For the sloshing problem, only the linear case is con-sidered. An interior boundary value problem is formulated associated to the six degreesof motions of the tank. The results obtained for both, the exterior and interior problemsare combined at the computation of the motion equation. As no damping is obtained inthe potential theory for the closed problem of the tank, we have modified the boundarycondition at the tanks walls, in order to include a dissipation parameter with the aim ofsimulating the energy disspation caused by viscous effects. This dissipation parametergives an artificial damping which should be calibrated against model tests results.

Formulations for second-order loads computations: The user of HydroStar is ableto choose between different formulations for the computation of second-order loads. Inaddition to the classical near-field and far-field formulation, the middle-field formulationhas been implemented. This formulation written on the control surface at some distancefrom the body, has the same virtue as the far-field formulation to have rapid numericalconvergence for horizontal drift loads. Furthermore, in the case of multiple bodies, thecontrol surface can be one surrounding an individual body and the wave loads applied onthe surrounded body are then obtained, while the far-field formulation provides only thesum of wave loads applied on all bodies and cannot give access to the wave loads on oneindividual body. An important application of the developed method is the multi-bodyinteraction.

Low-frequency loads in cross waves:In the common practice, only the long-crested seas are used for the design of floatingsystems. At the most, a directional spreading is considered for the first-order motions.At the first-order, the effects of directionality may be obtained by a simple sum of theeffects of the uni-directional waves independently. However, for the second-order loads,

Contents 03

the interaction between two waves coming from different directions may lead to additionalloading term that could represent an important part of the total second-order load actingon the system. In HydroStar , the near-field and the middle-field formulations have beenextended to the case of cross waves. Not only the mean drift loads, but also the full QTFof low-frequency loads can be computed.

In order to simplify the understanding of this user manual, the first two chapters provide pre-liminary information on the installation and conventions used in the software, followed by thechapters which are organized in the order of the execution of HydroStar in its common appli-cations.

Chapter 1

Getting Started

This chapter provides instructions for the installation of HydroStar and for making test runs inorder to check if the installation was well done.

1.1 Hardware configurationThe following minimum hardware configuration is necessary to run HydroStar :

PENTIUM 500MHz as a minimum; 100MB free on the Hard Disk ; 256MB RAM as a minimum; Windows 95, 98, 2000, NT , XP, Vista , 7 Graphic Card allowing OPENGL emulation.

1.2 InstallationIn order to install HydroStar , the user must follow the steps below:

log on with Administrator privileges (required for Windows XP); Run the Setup.exe program (the setup of HydroStar can be now downloaded on the

website www.veristar.com).

the user also needs a license file that is provided by Bureau Veritas.

If theres any problem in installing HydroStar please contact the following support peopleat Bureau Veritas:

11


Xiao-Bo Chen e-mail: [email protected] tel: +33 (0)1 55 24 74 74Guillaume de-Hauteclocque e-mail: [email protected] tel: +33(0)1 55 24 74 71

1.3 HydroStar interfaceAfter having installed HydroStar , a short cut of the program will be created in the users com-puter work area. Double click the icon and the following HydroStar DOS-like window will beopened.

===========****HydroStar For Experts V6.20****===========---------------------------------------(c)BV/DR 1991-2011

A new generation of hydrodynamic softwarefor offshore and naval applications

Hstar>>

To find out the working directory, type pwd and to change directory, just type cd path:

Hstar>>pwdC:/BVeritas/Hydrostar

Hstar>>cd c:/hydro/study

Additionally to this manual, HydroStar also provides an on-line manual. To access a list ofcommands just type man, and to access the description of one specific command just typeman followed by the name of the command.

===========****HydroStar For Experts V6.20****===========---------------------------------------(c)BV/DR 1991-2011

A new generation of hydrodynamic softwarefor offshore and naval applications

Hstar>>man

Chapter 1. Getting Started 13

1.4 Running testsSome test examples can be found in the folder /examples and can be used to check whetherthe program was correctly installed. The test examples also provide to the users the possibilityof using and modifying the input files for tutorial purposes.

To run the test examples the user may follow the instructions provided in the following chaptersof this manual.

Chapter 2

Overview

HydroStar is a powerful 3D diffraction/radiation potential theory 3-D panel software for wave-body interactions taking into account multi-body interaction, effects of forward speed anddynamic effects of liquid motions in tanks. Evaluation of 1st and 2nd order wave loads, mo-tions, accelerations, relative motions, wave elevation is dedicated to all structure systems indeep and finite depth waters with or without speed.

HydroStar is conceived to enhance technical excellence and productivity. It brings togethernumerous advantages and functionalities to meet high level requirements:

Rapid results as it uses efficient advanced algorithms

Elimination of irregular frequencies

Mixed panel - beam model

Multi-body interaction

Wave tank effect and wave attenuation in harbor

Inputs for air gap analysis, green water & slamming estimation

Linear and non-linear wave loads

Multi-directional second order loads

Dynamic effects of liquid motion in tanks

Account for resonant effects of moonpool

Automatic Transfer of Hydrodynamic pressure loads to FEM;

Fully interfaced with VeriStar Offshore mooring and structural software

21


2.1 HydroStar structureHydroStar is structured into the following main modules:

hslec : reading the mesh;Input: bodys geometry (coordinates, panel connectivity and condition of symmetry);Output: hydrostatic properties of the body (Volume, center of buoyancy, wetted surface,waterplane area and inertia, etc.);

hsrdf : radiation and diffraction computation;Input: wave conditions (wave frequencies and headings, water depth);Output: elementary solutions including added-mass, radiation damping and wave excita-tion loads;

hstnk : radiation computation inside a tank;Input: same as for hsrdfOutput: added mass for each tank included in the calculation.

hsmec : motions computation;Input: mechanic properties (mass distribution, additional stiffness and additional damp-ing matrices);Output: motions of floating bodies;

hsdft : second-order drift computation in uni-directional waves;Input: choice of formulation type (far-field, near-field or far field);Output: second order drift loads in uni-directional waves;

hsmdf : second-order drift computation in bi-directional waves;Input: choice of formulation type (near-field or middle field);Output: second order drift loads in bi-directional waves;

hsamg : pre-processing for second-order low-frequency computation in uni- and bi-directionalwaves;Input: choice of formulation type (near-field or middle field); difference-frequencies andwave frequencies for the computation.Output: input files for hsqtf ;

hsqtf : second-order low-frequency computation in uni- and bi-directional waves;Input: choice of formulation type (near-field or middle field); difference-frequencies andwave frequencies for the computation.Output: second order low-frequency loads in uni- and bi-directional waves;

Chapter 2. Overview 23

hsprs : pressure computation;Input: Coordinates of points to compute the pressure;Output: Pressure at the given points;

hswld : computation of global wave loads;Input: mass distribution along the ship (sections where the efforts are required);Output: efforts per defined station;

hsrao : construction of the transfer functions;Input: choice of which transfer function the user want to construct and the name of thefile to store the results;Output: transfer functions of motions, velocities, accelerations and second order loads;

hswav: wave visualization;Input: free surface mesh and wave components to visualize;Output: input data files of VSHIP for simulation of vessels motions and waves;

hsfem: transfer of hydrodynamic pressure loads to FEM;Input: whole ship finite element model and wave conditions (heading and frequency);Output: real and imaginary parts of hydrodynamic pressure loads.

hspec: Spectral analysis of short and long term;Input: wave data, etc;Output: spectral results.

Some secondary modules are available in addition to the ones listed above. Those modulesare used or for pre-processing purpose or for checking any result at intermediate stage of thecalculation.

hsmsh : mesh generator for simple geometries;Input: main dimensions of the body (barge, sphere, etc);Output: input file for hslec ;

hschk : verification of the mesh;Input: output of hslec ;Output: check of mesh (inconsistency, normal orientation, etc);

hvisu : visualization of the mesh;Input: output of hschk ;Output: view of the mesh;


hsinf : information about the mesh or information about mechanical computation;Input: output of hslec or output of hsmec ;Output: information about the mesh (like mean length of panels, etc) or informationabout mechanical computation (like frequencies, headings, etc);

hstat: hydrostatic properties verification and/or inertia matrices computation through aweight distribution;Input: Weight distribution (only needed for the calculation inertia matrices at givensections);Output: hydrostatic properties or/and input data for hsmec and hswld

hsrsn : resonance periods / frequencies computation;Input: output of hsmec ;Output: resonance periods / frequencies

hsplt: plotting of the RAOs;Input: output files from hsrao ;Output: graphic view of the RAOs


The figure 2.1 represents a scheme of HydroStar including all of its modules.

Figure 2.1: General scheme

2.2 Conventions used in HydroStarThe following coordinate system is used by HydroStar :

Axis Ox is positive in the forward direction; Axis Oy is positive to port side; Axis Oz is positive upwards.

The origin of the reference system used by HydroStar is at the free surface level. However, atany input file, the user is able to define the z-coordinates with respect to any other point (e.g.keel of the vessel). Lets call this additional reference system as user reference system.

The user reference system is only used for the input data. It needs to be parallel and withits origin at the same vertical line as HydroStar reference system. If the origin of the verticalaxis is not at the free surface, the user needs to input the keyword (ZFSURFACE) followed bythe z-coordinate of the free surface given in the user reference system. For example, the user


may define the z-coordinates of the mesh with respect to keel in the input for hslec if in thesame input file he defines ZFSURFACE equal to the draft. By default, the ZFSURFACE is equalto 0 corresponding to HydroStar reference system.

NOTE: The keyword ZFSURFACE should be used in every input file where the origin of theuser reference system is not at the free surface. The results are always given in HydroStarreference system (z=0 at the free surface).

The vessels translations surge, sway and heave are the motions in Ox, Oy and Oz respec-tively. The vessels rotations roll, pitch and yaw are defined as follows:

Roll is the rotation around the axis parallel to Ox through the reference point;

Pitch is the rotation around the axis parallel to Oy through the reference point;

Yaw is the rotation around the axis parallel to Oz through the reference point.

Regular incoming waves are described by their amplitude (a), frequency () in rad/s and head-ing (). The wave heading is defined by the angle between the propagation direction and thepositive direction of the axis Ox.

x

y

00

4590

135

180

225

270

315

AF Midship FP

Figure 2.2: Wave headings

A regular wave is defined by its analytical expression:

(X, Y, t) = a cos{t k[(X Xcal) cos + (Y Ycal) sin ]} (2.1)


with k the wavenumber determined by the dispersion equation:

k tanh(kH) = 2

g(2.2)

where, H is the water depth and g is the acceleration due to gravity.

If the wave reference point is taken equal to the calculation point, X = Xcal and Y = Ycal, theincident wave elevation is given by (see also fig 2.3):

(Xcal, Ycal, t) = a cos(t) (2.3)

t

elevation

Figure 2.3:

Any other physical value of responses like vessels motions is written in the way:

U(t) = u cos(t+ ) (2.4)

with the amplitude u and the phase . The ratio between the response amplitude and waveamplitude is called RAO:

RAO = u/a (2.5)

is often called as phase lead as it represents an advance comparing to waves. is the valueouput by HSRAO when specifying the keyword PHASE

NOTE 1 : Internally the phase convention is based on the incident potential (i = ag ei(kxt))so the incident wave height at the reference point is 0 = a cos(t+ pi2 ). The real and imaginary


part that can be output by HSRAO with keywords COS and SIN are linked to this conven-tion. This imply that phase 0 = arg(RAOcplx) is related to the wave 0 = a cos(t+ pi2 ), otherphysical values being given by U0(t) = u cos(t 0)

NOTE 2: Attention should be made to the definition of the wave reference point (REFWAVE)and to the calculation point, also called reference point (REFPOINT). The first one defines thepoint where the wave is zero ascendent at the instant zero. The other is the reference pointlocated on the body for the calculations. By default those points are taken equal to the centre ofbuoyancy for the radiation and diffraction computations (hsrdf ) and equal to centre of gravityfor the motions computations (hsmec ). Obviously all the results obtained in hsrdf in the centreof buoyancy are transferred to the centre of gravity, consistently, for the computations in hsmec .

2.3 Units used in HydroStarThe following units are used in HydroStar :

Length (L) mSurface (S) m2Volume (V ) m3

Mass (M) KgInertia (I) Kg.m2

Mass density (r) Kg/m3

Time (t) sGravity (g) m/s2

Wave frequency () rad/s (circular frequency)Wave period (T ) s

Wave amplitude (A) mWave heading () deg

Translations (T ) m Surge, sway and heaveTranslations RAO (T ) m/m

Rotations (R) deg Roll, pitch and yawRotations RAO (R) deg/m

Forces (F ) N(= Kg m/s2)Moments (M) N mPressure (P ) m in waterhead

Speed m/s

Chapter 3

Mesh Generation

HydroStar provides two automatic mesh generators for simple geometries. The first one is ded-icated to single simple geometries, such like cylinders, barges, spheres, ect. The second one isdedicated to bodies composed by several simple geometries.

In addition, the module AMG (Automatic Mesh Generation) provides the possibility of au-tomatic generation of ship meshes by just inputting the stations coordinates and some infor-mation about the aft and forward parts of the vessel. This module can be used independentlyfrom HydroStar .

3.1 Single simple geometry mesh generationThis module allows the user to generate the following geometries:

Cylinder

Semi-sphere

Elliptical cylinder

box

The following commands shall be input in HydroStar window for the generation of eachtype of geometry mentioned above:

Cylinder:i) Type hsmsh -cs[symmetry code]where:

31


symmetry code=0 if no symmetry=1 if symmetric around x axis=2 if symmetric around x and y axi

ii) HydroStar will then require the following values in order to define the mesh:R = radius of the cylinder;H = height of the cylinder;ntheta = number of panels along the circumference;nH = number of panels in the cylinder height;nR = number of panels in radial direction in the bottom of the cylinder.

Figure 3.1: Example of cylinder mesh

iii) HydroStar generates a file named cyls[symmetry code].dat with the appropriate for-mat already described here above.

Hstar>>cyl>>hsmsh -cs2R,H,ntheta(0->PI/2),nH,nR(fond)=: 15 40 20 20 15Output mesh file name : cyls2.dat

Semi-sphere:i) Type hsmsh -ds[symmetry code]where:

symmetry code=0 if no symmetry=1 if symmetric around x axis=2 if symmetric around x and y axi

Chapter 3. Mesh Generation 33

ii) HydroStar will then require the following values in order to define the mesh:R = radius of the cylinder;ntheta = number of panels along the circumference around z axis;nphi = number of panels along the circumference around x / y axis

Figure 3.2: Example of sphere mesh

iii) HydroStar generates a file named dsphs[symmetry code].dat with the appropriate for-mat already described here above.

Hstar>>dsphe>>hsmsh -ds2R,ntheta(0->PI/2),nphi = : 10 20 20Output mesh file name : dsphs2.dat

Elliptical Cylinder:i) Type hsmsh -es2ii) HydroStar will then require the following values in order to define the mesh:

a = length of the elliptical cylinder;b = breadth of the elliptical cylinder;H = height of the elliptical cylinder;ntheta = number of panels along the circumferencenH = number of panels in height;nR = number of panels in radial direction in the bottom of the cylinder.

iii) HydroStar generates a file named cyls2.dat with the appropriate format already de-scribed here above.

Hstar>>ellyp>>hsmsh -es2a,b,H,ntheta(0->PI/2),nH,nR(fond) = : 20 10 10 20 10 10Outputmesh file name : cyls2.dat

Box:


Figure 3.3: Example of elliptical cylinder mesh

i) Type hsmsh -bteii) HydroStar will then require the following values in order to define the mesh:

L = length of the box;B = breadth of the box;T = height of the box;nL = number of panels in length;nB = number of panels in breadth;nT = number of panels in height.

Figure 3.4: Example of box mesh

iii) HydroStar generates a file named boite.don with the appropriate format already de-scribed here above.

Hstar>>boite>>hsmsh -bteL,B,T= : 20 10 5nL,nB,nT= : 20 10 5Output mesh file name : boite.don


3.2 Bodies composed by various simple geometriesThe user can use several simple geometries to compose a single body. In this case, an input fileshall be generated with the following keywords:

TYPE 1

SYMMETRY isym (=1 for symmetry XZ= 2 for symmetry XZ and symmetry YZ)

ZFSURFACE zfs (z coordinate of the free surface, default = 0)

NODE id nd x y z (id number of the node, x, y and z coordinates)

OBS: This module only generates the mesh up to the free surface level.

The user may define rules for the discretization of the mesh. This option allows to refinethe mesh close to the free surface and/or close to the keel.

RULE id rl cos(A1) cos(A2) (Rule for the refinement of the mesh)

where:cos(A1) is the cosine of the first refinement anglecos(A2) is the cosine of the second refinement angle

The principle for refinement are explained in figure 3.5.

For example, if the user defines RULE 1 0.0 0.0, which corresponds to A1 =90 and A2 =90,the mesh will be uniform. If the user defines RULE 1 0.90 0.0 the mesh will be more refinedat the left side.

After defining nodes and rules for the refinement of the mesh, the user can define elementsor geometries to be meshed. Different elements can be used and composed together into asingle mesh:


Figure 3.5: Refinement of the mesh

PATCH: A patch is a flat panel described by four nodes A B C D. In case of triangles, onenode should be repeated in the definition of the panel. The normal is oriented followingthe right-hand rule.

A patch is defined as below:

PATCH id element NODE id nd(A) id nd(B) id nd(C) id nd(D) AB NB nb el(AB) AB RULEid rl(AB) BC NB nb el(BC) BC RULE id rl(BC)

where:

nb el(AB) & nb el(BC) correspond to the number of elements along the side from nodeA to node B and the number of elements along the side from node B and C, respectively.

id rl(AB) & id rl(BC) correspond to the refinement rule applied to the sides AB and


BC, respectively.

Figure 3.6: Patch Definition

As an example, a barge can be decomposed in several PATCHS like in figure 3.7 below:

Figure 3.7: Barge

CIRSEG: This type of element is used to represent a segment of circle as in the figure3.8, where C is the node at the centre of the circle, R is the radius of the circle. A and Bare the two nodes that compose the segment. A segment of circle is defined as below:


CIRSEG CTR id nd(C) RAD R ANG ang1 ang2 NODE id nd(A) id nd(B) C NB nb el(AB)C RULE id rl(AB) H NB nb el(R) H RULE id rl(R)

where:

ang1 & ang2 are the first and last angle for the definition of the segment, respectively.In the figure 3.8 the first angle is 0 deg and the last angle is 90 deg.

nb el(AB) & nb el(R) correspond to the number of elements in the segment from nodeA to node B and the number of elements in the direction of the radius of the circle (R),respectively.

id rl(AB) & id rl(R) correspond to the identification number of refinement rule appliedin the direction of the segment AB and in the direction of the radius R respectively.

Figure 3.8: CIRSEG Definition


CIRCYL: Its used to generate vertical cylinders or segments of cylinders like in figure3.9. The following keywords are used to define a cylinder or a part of it:

CIRCYL CTR id nd(A) id nd(B) RAD radius(A) radius(B) ANG ang1 ang2 C NB nb el(arc)C RULE id rl(arc) H NB nb el(height) H RULE id rl(height)

where:

radius(A) & radius(B) are the radius of the cylinder at the horizontal plane passingby node A, and the radius of the cylinder at the horizontal plane passing by node B,respectively. In this way the radius of the cylinder may vary along its height.

ang1 & ang2 are the first and last angle for that define the cylinder in degrees. Forexample, a cylinder with ang1 = 0.0 and ang2 = 360.0 means a complete cylinder.

nb el(arc) & nb el(height) correspond to the number of elements along the arc of thecylinder and along the height of it, respectively.

id rl(arc) & id rl(height) correspond to the identification of the refinement rule alongthe arc of the cylinder and along the height of it, respectively.

Figure 3.9: CIRCYL Definition


3.2.1 Example of Input file for hsmshThe figure 3.10 gives an example of input for the module hsmsh where several simple geometriesare used to composed a mesh.

TYPE 1 #For the type of mesh definition as described aboveSYMMETRY 2 #Number of symmetries

ZFSURFACE 42.0 #Position of free surface

#Nodes for the definition of the mesh (up to free surface only)NODE 1 0.000 0.000 0.000NODE 2 0.000 0.000 4.000NODE 3 0.000 0.000 42.000NODE 4 26.625 0.000 0.000NODE 5 18.830 18.830 0.000NODE 6 0.000 26.625 0.000

#Refinement RulesRULE 0 0.00 0.00 #Uniform meshRULE 10 -0.95 0.00RULE 99 -0.95 0.95

#Elements of the meshPATCH 1 NODE 1 6 5 4 AB NB 8 AB RULE 0 BC NB 8 BC RULE 0CIRSEG CTR 1 RAD 46.625 ANG 0.0 45.000 NODE 4 5 C NB 8 C RULE 0 H NB 10 H RULE 10 INVERSECIRSEG CTR 1 RAD 46.625 ANG 45.0 90.000 NODE 5 6 C NB 8 C RULE 0 H NB 10 H RULE 10 INVERSECIRCYL CTR 1 2 RAD 46.625 46.625 ANG 0.0 90.0 C NB 16 C RULE 0 H NB 3 H RULE 99CIRCYL CTR 2 2 RAD 43.500 46.625 ANG 0.0 90.0 C NB 16 C RULE 0 H NB 3 H RULE 99 INVERSECIRCYL CTR 2 3 RAD 43.500 43.500 ANG 0.0 90.0 C NB 16 C RULE 0 H NB 20 H RULE 99

ENDFILE

Figure 3.10: Input file for hsmsh

NOTE: When the keyword INVERSE is used at the end of the command lines used to gen-erate the elements of the mesh, it means that the orientation of the normal vector is inversed.

3.2.2 Generating the mesh using hsmshAfter constructing the input file as explained in the above items, the user is ready to constructthe mesh by using the following commands in HydroStar window:

Hstar>>hsmsh inputfile

Immediately after running hsmsh the user may visualize the mesh generated by typing:Hstar>>hvisu

The figure 3.11 represents the mesh generated using the example file in figure 3.10.


Figure 3.11: Example of mesh generated using hsmsh

The input file for hslec named proj.hst is generated in the working directory.

3.3 Use AMG to generate MeshAMG (Automatic Mesh Generation) is delivered in the HydroStar package. To generate meshusing AMG, use the command hsmsh -ship. For additional information about AMG, pleaserefer to the AMG user manual.

Hstar>>hsmsh -ship input

3.4 Mesh equilibriumThe displacement of the mesh input in HydroStar must correspond to the mass later described.Althought it is better to generate a mesh directly at the equilibrate draft and trim, the toolhsbln can be used to get a balanced mesh from mesh input up to the deck.

INPUT MESH Input mesh (up to the deck)OUTPUT MESH test.hst Output balanced meshCOGPOINT BODY 1 134.126 0.0 4.971 Position of the center of gravity in the Input mesh reference systemMASS BODY 1 118992250.0 id of the body , Mass of the body

Be carefull : In the new mesh reference the position of the center of gravitywill be changed !

Compared to a mesh directly generated at the equilibrate draft, the panel near the freesurface can not be as regular and refined.

Hstar>>hsbln input.bln

Chapter 4

Reading the Mesh

The input of the mesh is performed by HydroStar using the module hslec (see fig 4.1).

Project

hschk

hslec

Figure 4.1: hslec

To run this module, the user is supposed to have already prepared the mesh. For prepara-tion of the mesh, refer to Chapter 3.

The hull geometry shall be represented by flat quadrilaterals or flat triangulars with the normalvector oriented towards the fluid (see fig 4.2).

4.1 Input file formatThe format of the definition of the nodes coordinates in the input file is as follows:

41


n1n1

n2n2

n3n3

n4

n

n

Figure 4.2: Flat quadrilaterals and flat triangulars

.

COORDINATES

[no node], x no, y no, z noENDCOORDINATES

where:

no node sequential number of the node;

x no x coordinate of the number no;

y no y coordinate of the number no;

z no z coordinate of the number no.

The format of the definition of the panel connectivity in the input file is as follows:

PANEL TYPE itype

[no panel], n1 panel, n2 panel, n3 panel, n4 panel

ENDPANEL

where:

Chapter 4. Reading the Mesh 43

itype =0 where no panel is not given=1 where no panel is givenno panel = sequential number of the paneln1 panel = node number of the first cornern2 panel = node number of the second cornern3 panel = node number of the third cornern4 panel = node number of the forth corner

The following key words shall be used in the input file for hslec module:

COORDINATES start line of node definitionENDCOORDINATES end line of node definition

PANEL start line of panel definitionENDPANEL end line of panel definition

ENDFILE to end the input file.


The following keywords may be input as optional commands:

PROJECT project title (default= project)USER users name (default= anonym)

REFLENGTH reference length (default= 1.0m)

GRAVITY gravity acceleration constant (default= 9.81m/s2)RHO fluid mass density (default= 1025kg/m3)

NBNODES number of nodes (default= no of lines onthe nodes definition)

NBPANEL number of panels (default= no of lines onthe panels definition)

NBBODY number of bodies (default= 1)

NFHULL number of panels of the bodys hull (default= NBPANEL)

SYMMETRY number of symmetry (default=0)

NUMPANEL start number and end number (default= 1 toof panels NBPANEL)

NUMFHULL start number and end numberof the hull panels

NUMFPONT start number and end numberof the panels above the hull

NFSWATER number, start number and endnumber over the interior waterplane

NFREESURFACE number, start number and endnumber of panels over the free surface

ZFSURFACE coordinate of the freesurface in the userreference system (see item 2.2)

(default= 0)

COEFZ0 ratio of the panel size of the waterplanemesh and of the hull mesh (default=1.5)

ZONEDAMPING xmin xmax dltx ymin ymax dlty epslon dissipation zone


The figure (see fig 4.3) contains an example of the input file for hslec .

PROJECT LNG CARRIER - Full Loaded case T=12.350mUSERS BV

NBBODY 1SYMMETRY BODY 1 1RHO 1025.0GRAVITY 9.81

COORDINATES TYPE 01 0.10005E+02 0.00000E+00 -0.10821E+022 0.10005E+02 0.11428E+01 -0.92114E+01.. .. .. ..ENDCOORDINATES

PANEL TYPE 01 2 17 162 3 18 17.. .. .. ..ENDPANEL

ENDFILE

Figure 4.3: Input file for hslec

In the following sections of this chapter, some specific fonctionalities on the input of the meshare described in more details.

4.2 Input file for a single bodyThe input file for a single body may contain only the part of the body below the waterline or thecomplete ship mesh containing the parts below and above waterline and even superstructure.The upper parts of the mesh are used for visualization purpose only.

In case the mesh generated contains also the part of the vessel above the waterline, the meshshould be divided into two parts: the submerged part actually used in the calculations and theupper part only used for visualization. It means that during the construction of the mesh allpanels and nodes composing the submerged part should be grouped together in one block ofdata (nodes and coordinates). In addition, there should be no panels cutted by the free surface.

When defining coordinates and nodes of the mesh, the user needs to specify which panelscompose the submerged part and which panels compose the upper part by given the first andlast panel number of each part.


For that, the following keywords should be used:

NUMFHULL nb body, ni hull, nf hull number of the body, start number andend number of hull panels

NUMFPONT nb body, ni pont, nf pont number of the body, start number andend number of panels above waterline

The file displayed in figure 4.4 exemplifies the input file for hslec considering also the partof the body above waterline.

PROJECT: SHIPUSER: BV

NBBODY 1SYMMETRY BODY 1 1NUMFHULL 1 1 2105NUMFPONT 1 2106 3758

COORDINATES TYPE 01 0.000000 0.000000 0.0000002 8.140500 0.000000 -11.444000.. .. .. .... .. .. ..3918 5.490700 0.000000 -10.8740003919 5.577100 0.000000 -6.665400ENDCOORDINATES

PANEL TYPE 02 3 37 363 4 38 37.. .. .. .... .. .. ..3433 3434 3908 39073434 3435 3909 3908ENDPANEL

ENDFILE

Figure 4.4: Example considering the part of the body above waterline

In the file above, the part of the hull below waterline is defined by the panels from 1 to2105 identified by the keyword NUMFHULL, while the part of the hull above the waterline isdefined by the panels from 2106 to 3758 that can be identified by the keyword NUMFPONT.In this case all the coordinates of nodes and panels are defined together, although the usercan clearly observe that the data can divided in two blocks. Another possibility is to repeatthe keywords COORDINATES & ENDCOORDINATES and PANELS & ENDPANELS to define asmany blocks of data as wanted.


4.3 Input file for multi bodiesAny number of bodies can be modelled in HydroStar . The user has to define the number ofbodies and the first and last identification numbers of the panels associated to each body. Thecoordinates and panels of each body can be defined separately, however in the same file.

The symmetry property is not used in the case of multi-body mesh. The whole hull should bemodelled.

Its important to remark that the identification numbers of the nodes shall be unique. Itmeans that, in principal, there should be only one node with a certain identification number.However, in case of multi-body its normally the case that the meshes are prepared separatelyand the nodes number may be repeated for the two meshes. In order to solve this problem,the keyword NODE0 is used after the keywords COORDINATES and PANELS to shift the nodesnumbers by the value defined after NODE0 and to guarantee that theres no other node withthe same number.

Another useful possibility is to translate (in x- and y- direction) and rotate the mesh (in thehorizontal plane) by using the keywords TRANS and ROTA after the keyword COORDINATES.

The reference systems are centered on the reference point of each body, but the axis remainparallel to the global mesh reference system.

The file displayed in figure 4.5 gives an example of input file for hslec .


Mesh by AMG from input file :

NBBODY 2NUMPANEL 1 1 728NUMPANEL 2 2537 4942NUMFPONT 1 729 2536NUMFPONT 2 4943 7304

COORDINATES TYPE 01 0.83862E+01 0.00000E+00 -0.43537E+012 0.83862E+01 0.64438E+00 -0.37057E+01.. .. .. .... .. .. ..6889 0.23743E+03 0.00000E+00 0.18145E+026890 0.23743E+03 0.00000E+00 0.18145E+02ENDCOORDINATESPANEL TYPE 01 2 21 202 3 22 21.. .. .. .... .. .. ..6851 6808 6807 68506852 6809 6808 6851ENDPANEL

COORDINATES TYPE 0 TRANS 0.0 -50.0 ROTA 0.2 NODE0 100001 0.66550E+01 0.00000E+00 -0.15991E+022 0.57373E+01 0.00000E+00 -0.13585E+02.. .. .. .... .. .. ..15565 0.27322E+03 0.00000E+00 0.59000E+0115566 0.27322E+03 0.00000E+00 0.59000E+01ENDCOORDINATESPANEL TYPE 0 NODE0 100001 2 23 222 3 24 23.. .. .. .... .. .. ..15502 15435 15434 1550115503 15436 15435 15502ENDPANEL

ENDFILE

Figure 4.5: Example of input file for multi bodies

In the example file in figure 4.5, the command TRANS is used to translate the nodescoordinates of the second body by 0.0m in the longitudinal direction and by 50.0m in thetransverse direction. The keyword ROTA is used to rotate the mesh by a angle of 0.2deg in thehorizontal plane. Thus, the nodes coordinates given in the input file are modified as follows:

x no = x no cos() y no sin() + trans xy no = y no sin() + y no cos() + trans y

Also, it should be noticed that the nodes numbers given for the two bodies are repeated.In this case, the keyword NODE0 has been used to shift the nodes numbers of the secondbody by a value of 10000 which has been considered sufficiently big to avoid having twonodes with the same number. In fact the nodes numbers of the second body will be equalto no node=no node+no NODE0


The mesh described in figure 4.6 can be obtained.

Figure 4.6: Two bodies meshes

4.4 Input file including dissipation zoneIn a confined zone, such like moonpool or gap between two ships in side-by-side configura-tion, the hydrodynamic interaction may create violent wave kinematics at certain frequencies.Within the framework of the potential theory theres no limit in predicting resonant waveelevation while in reality the resonant motion is largely damped by different mechanisms ofdissipation. In HydroStar , its possible to include a dissipation term in the fluid in order tosimulate the effects of viscous damping. This dissipation parameter is artificial and should becalibrated against measurements. In addition, the use of this term requires the meshing of thefree surface at the region where wave kinematics are most important.

The mesh of the damping zone is made by HydroStar. It can have rectangular or circularshape. The following keywords should by included in the input file for hslec :


ZONEDAMPING xmin xmax dltx ymin ymax dlty epslon

where:

xmin is the minimum x-coordinate of the rectangular damping zone

xmax is the maximum x-coordinate of the rectangular damping zone

dltx is the length of the panels of the damping zone mesh

ymin is the minimum y-coordinate of the rectangular damping zone

ymax is the maximum y-coordinate of the rectangular damping zone

dlty is the width of the panels of the damping zone mesh

epsilon is the dissipation parameter


Figure 4.7: Rectangular dissipation zone

And the circular damping zone:

ZONEDAMPING rmin rmax dltr min max dlt epslon CTR xctr yctr

where:rmin is the minimum radius value of the circular damping zone

rmax is the maximum radius value of the circular damping zone

dltr is the length of the panels of the damping zone mesh in the radial direction

min is the minimum angle in degrees of the circular zone damping

max is the maximum angle in degrees of the circular zone damping

dlt is the delta angle of for the panels definition of the circular damping zone mesh


epsilon is the dissipation parameter

CTR xctr yctr Coordinates of the centre of the circular zone

The file displayed in figure 4.8 gives an example of input file for hslec including a circulardamping zone. The user may include several damping zones by repeating the command lineZONEDAMPING.

PROJECT MONOCOLUMN

ZONEDAMPING 0.0 34.5 3.45 0.0 90.0 7.50 0.10 CTR 0.0 0.0

SYMMETRY BODY 1 2NUMPANEL 1 1 468

ZFSURFACE 38.0COORDINATES TYPE 01 47.50000 0.00000 0.000002 47.09363 6.19999 0.00000.. .. .. .... .. .. ..1727 5.22105 39.65779 50.000001728 0.00000 40.00000 50.00000ENDCOORDINATESPANEL TYPE 01 2 21 202 3 22 21.. .. .. .... .. .. ..1723 1724 1726 17251725 1726 1728 1727ENDPANEL

ENDFILE

Figure 4.8: Example of input file including zone damping


4.5 Input file including tanksIn case the user wants to solve the coupled sloshing-seakeeping problem, the tanks walls up tothe filling level need to be meshed and included into the input file of hslec .

In addition to the keywords used to described in the above sections, the following keywordsshould be included to the input file for hslec with the aim of defining the mesh of the tank(s):

NBTANK nb tanks Number of tanks meshedSYMMTANK id tk sym define the symmetry of a defined tank

id tk : identification number of the tanksym = 0 (no symmetry)sym = 1 (symmetry around XZ plan)

NUMTANK id tk first panel last panel z fsf where:id tk: identification number of the tankfirst panel: number of the first panel that de-fines the tank meshlast panel: number of the last panel that de-fines the tank meshz fsf: z-coordinate of the tank free surfacewith respect to the local system

REFPTANK id tk x ref y ref z ref rho where:id tk: identification number of the tankx ref , y ref , z ref: coordinates of the originof the tank mesh with respect to the originof the hull meshrho: density of liquid in the tank in kg/m3

The coordinates and panels of the tanks are defined in the same way as for the hull mesh.The normal vectors of the panels used to describe the tanks are defined towards the fluid insidethe tank. The tanks meshes may be defined with respect to any point. By default the origin ofthe tank mesh reference system is assumed to be at the free surface of the tank, otherwise thevalue z fsf should be provided in order to define the position of the free surface with respectto the origin chosen to describe the tank mesh. The REFPTANK defines the coordinates of theorigin of the tank mesh in the hull mesh reference system.

For the definition of the panels of the tanks another value can be defined at the end of thecommand line as below:


.

PANEL TYPE itype NODE0 node0[id panel] node1 node2 node3 node4 epsilon where:

id panel: defined when itype=1node1 node2 node3 node4 : identificationnumbers of the four nodes that compose thepanels.epsilon: dissipation parameter associated tothe panel (typically around 0.01)

ENDPANEL

It should be mentioned that for the radiation problem inside the tanks, no damping is obtained.However, in reality the energy is dissipated by viscous effects. The dissipation parameter ep-silon is used to simulate the effects of the viscousity within the assumptions of the potentialtheory. Its in fact an artificial damping and the epsilon parameter needs to be calibratedagainst model tests. In addition, in this method, all the dissipation is assumed to occur at thetanks walls.

The figure 4.9 presents an example of input file for hslec including two tanks. In this examplethe origin of the tanks reference systems is located in the aft bulkhead and at the bottom ofeach tank. In this way the value z fsf defines the z-coordinate of the free surface of the tankwith respect to its bottom. Also in this example the REFPTANK coordinates are in fact thecoordinates of a point located at the centreline of the tank, at the aft bulkhead and at thebottom of the tank expressed in the global system.


PROJECT TANKS

USER BV

SYMMETRY BODY 1 1NUMPANEL 1 1 1210

NBTANK 1SYMMTANK 1 2NUMTANK 1 1211 2366 1.42REFPTANK 1 168.0 0.0 0.0 1025.0

COORDINATES TYPE 01 0.00000E+00 0.00000E+00 0.00000E+002 0.81405E+01 0.00000E+00 -0.11444E+02......3918 0.54907E+01 0.00000E+00 -0.10874E+023919 0.55771E+01 0.00000E+00 -0.66654E+01ENDCOORDINATESPANEL TYPE 02 3 37 363 4 38 37......3433 3434 3908 39073434 3435 3909 3908ENDPANEL

COORDINATES TYPE 0 NODE0 100001 0.00000 0.00000 0.000002 0.00000 0.98577 0.00000......233 10.91600 9.97858 1.33572234 10.91600 10.51600 1.87200ENDCOORDINATES

PANEL TYPE 0 NODE0 100001 2 11 10 0.010002 3 12 11 0.01000......232 233 229 228 0.01000233 234 230 229 0.01000ENDPANEL

ENDFILE

Figure 4.9: Example of input file including tanks


4.6 Input file of hybrid model

Hybrid model is the one composed by panels and beams mixed in the same model. HydroStaruses the potential theory for the panels and Morison formulation for the beams.

To model the beams, the user shall define its coordinates, properties and number of segmentsthrough the following commands:

PROPBEAM

no prop, beam type, properties

ENDPROPBEAM

where:no prop is the number of the beams group that owns the same propertiesbeam type defines the shape of the beam and the commands RECT or CIRC

shall be used

If beam type = RECTthen properties shall be defined by: width, Cmz, Cdz, height, Cmy,Cdy, water density.

If beam type = CIRCthen properties shall be defined by: diameter, Cm, Cd, water density.

BEAM TYPE itype

[no beam], n1 beam, n2 beam, no prop, no seg

ENDBEAM

where:


itype = 0 where no beam is not given= 1 where no beam is given

no prop = is the number of the beams group that owns the same properties

no seg = is the number of segments in which the beam shall be

The user may make use of fictitious beams to model elements that are already modelled throughpanels. Fictitious beams are the ones without mass (Cm = 0) but with damping coefficientdifferent than zero (Cd > 0). This way the additional drag efforts will be added in the dampingmatrix, without changing the inertia matrix.

The input file in fig 4.10) exemplifies the hybrid model input file exemplifies for hslec. Theexample corresponds to a semi-submersible, in which the pontoons and columns are modelledby fictitious beams with Cm = 0.

The mesh obtained is displayed in figure 4.11.

4.7 Reading the input fileConsidering that the mesh file (e.g. shiplec.don) is stored in one work directory, e.g. c:/hydro/study,the user has to execute the following steps in order to perform the reading of the mesh inputfile:

Go to the work directory where the file is stored (see item 1.3 for information);Before reading the mesh, the user needs to create a project. the project name chosen isused to name all the binary files generated by HydroStar and used as input files for thevarious modules as well as the control files that give intermediate results of the calcula-tions.

To create a new project for which the results are stored (if the project is not created, thedefault name used by HydroStar is PRO):

Hstar>>proj shipHstar>ship>

If other projects already exist in the working directory, the user may list all the ex-isting projects by typing:


PROJECT SEMI-SUBUSER BV

SYMMETRY BODY1 1

PROPBEAM1 RECT 14.0 0.0 1.2 6.1 0.0 0.7 1025.02 CIRC 9.4 0.0 0.8 10253 CIRC 2.0 1.0 0.8 10254 CIRC 1.8 1.0 0.8 10255 CIRC 1.6 1.0 0.8 1025ENDPROPBEAM

BEAM TYPE 11 5007 5001 5 52 5010 5004 5 5.. .. .. .. .... .. .. .. ..20 5039 5040 2 15ENDBEAM

COORDINATES TYPE 0# Node for beam definition5001 33.50000 14.28100 0.000005002 33.50000 -14.28100 0.00000.. .. .. .... .. .. ..5040 -33.50000 -27.50000 -15.50000# Nodes for panel definitons1 3.95000E+01 3.42500E+01 -2.14000E+012 3.95000E+01 3.45000E+01 -2.09500E+01.. .. .. .... .. .. ..441 0.00000E+00 3.22000E+01 -1.55000E+00ENDCOORDINATES

PANEL TYPE 11 4 36 48 472 36 174 175 48.. .. .. .. .... .. .. .. ..414 439 441 368 377ENDPANEL

ENDFILE

Figure 4.10: Example of input file for hybrid model

Hstar>>lsproj

To read the input file using hslec name file command:

Hstar>ship>hslec shiplec.don

It will appear, in HydroStar window, the values used as input data, the reference point ofincident wave and the positions of the reference point and the centre of buoyancy.


Figure 4.11: Hybrid model of a Semi

4.8 Getting information about the meshAfter reading the mesh, the user may get some information about it by typing:

Hstar>proj>hsinf -g

The following information are displayed at the screen:

Xmin, Xmax and Length of the mesh; Ymin, Ymax and Breadth of the mesh; Zmin, Zmax and Depth of the mesh; Number of symmetries; Number of panels; Body surface; Average panel surface; Average panel length;


Bodys volume;

Centre of buoyancy

4.9 Preliminary verificaton of the meshAfter the execution of the above steps, the user has to perform a preliminary check of the meshby simply typing the command hschk (see fig 4.12):

Hstar>proj>hschk

The following verifications will be performed:

Consistency of the normal vector orientation;

Panels with null area;

Panels over the free surface;

Panels at free surface;

Overlapped panels;

Holes (neighbor-absences);

hschk

hsrdf

hslec

Figure 4.12: hschk

A report is printed on the screen giving the number of panels presenting any inconsistency.


4.10 Checking the hydrostatic propertiesThe computation of the hydrostatic properties is very useful to check the correspondence of themodel with the real vessel characteristics. To run this computation and display the results onthe screen the user has only to type the command hstat :

Hstar>proj>hstat

hschk

hsrdf

hstat

Figure 4.13: hstat

The following properties are then calculated:

Hull Volume; Wetted Hull Surface; Waterplane Area; Waterplane Inertia; Distances between the centre of buoyance and the metacentre (BM).

4.11 Visualization of the meshThe visualization of the mesh is performed by VISU4D by just typing the command hvisu inHydroStar window (see fig 4.15):

Hstar>proj>hvisu

Another window will be opened for VISU4D with the mesh read by HydroStar (see fig 4.16).


Figure 4.14:

hschk

hsrdf

hvisu

Figure 4.15: hvisu

In order to visualize the upper part of the mesh and the water-plane mesh given in inputfile, the user has to type the command:

Hstar>proj>hvisu -t

And then obtain a picture of the complete mesh (see fig 4.18).

In case tanks are included in the input file for hslec, the user may visualize the hull mesh(figure 4.17) together with the tanks by typing:


Figure 4.16:

Hstar>proj>hvisu -T

NOTE: The command hvisu -T with T in capital letter (for the visualization of tanks) shouldnot be confused with the command hvisu -t (for the visualization of upper part of hull and meshfor elimination of irregular frequencies).


Figure 4.17:

Theres also the possibility of visualizing only a part of the mesh by typing:

Hstar>proj>hvisu -c

Then, the point where the user wants to cut the mesh will be required:

Type xcut, ycut or zcut and Value

Through VISU4D, the user is able to change the visualization mode, the point of view, tozoom in and out and rotate the mesh in a very user-friendly interface.

Please refer to appendix C in order to get more details about the use of VISU4D.


Figure 4.18:

Chapter 5

Diffraction radiation computation

The radiation solutions are the potential flow around the vessel when the vessel moves in theotherwise quiescent fluid. The added-mass is defined by the load on the vessel due to its unitacceleration while the radiation damping is the ratio between the load and vessels velocity.The matrices of added-mass and radiation damping are of 6 x 6 dimensions for a single bodyand 6N x 6N dimensions for multi-body, where N is the number of bodies.

The diffraction solutions are the potential flow around the vessel remaining immobile in in-coming waves. The wave excitation loads are obtained by integrating the dynamic pressure onthe fixed vessel in incoming waves.

The module hsrdf of HydroStar solves the problem of diffraction and radiation around fixedand floating bodies and its based on the following:

First and second order potential theory of free surface flow; Integral equations / boundary element method; Efficient evaluation of associated Green functions; Elimination of irregular frequencies; Independency of the mechanic properties of the system.

The module hsrdf can be run after the module hslec.In case of seakeeping-sloshing coupled analysis, in addition to the module hsrdf for the

exterior problem, the module hstnk is used after hsrdf to solve the radiation problem inside thetanks.

51


5.1 Input fileThe following data have to be provided to perform radiation and diffraction computation:

Extension of the file that will store the results; Wave frequencies (rad/s); Wave headings (deg); Water depth (m) or infinity water depth.

The following data may be inputted as optional parameters:

Reference length; Acceleration due to gravity; Water mass density.

Chapter 5. Diffraction radiation computation 53

The following keywords shall be used in the input file for hsrdf execution:

FILENAME file name extension of the file to identify therun

FREQUENCY TYPE itype start line to give wave frequenciesfrequency linesENDFREQUENCY end line to give wave frequencies

If itype = 0,frequency lines = no freq, freq1 one frequency per line with iden-

tificationnumber

If itype = 1,frequency lines = freq1, freq2, freq3... several frequencies at the same

linewithout identification number

If itype = 2,

frequency lines =WMIN min freq minimum frequencyWMAX max freq maximum frequencyWSTP step freq Step of wave frequency

HEADING TYPE itype start line to give wave headingsheading linesENDHEADING end line to give wave headings

If itype = 0,heading lines = no head, head1 one heading per line with identi-

fication numberIf itype = 1,heading lines = head1, head2,head3... several headings at the same line

without identification numberIf itype = 2,

heading lines =HMIN min freq minimum headingHMAX max freq maximum headingHSTP step freq step of wave headings

ENDFILE to end the hsrdf file


The following keywords are optional:

NBFREQUENCY no freq total number of wave frequenciesNBHEADING no head total number of wave headingsWATERDEPTH value depth water depth value or infinite (default = inf)

or inf

REFPOINT BODY x ref, y ref, z ref reference point of the body (COB;0)REFWAVE x wave, y wave reference point for incoming waves (COB;0)

ELIMIRREG YES or NO option of eliminating irregular frequencies(default=YES)

SPEED start line to give speed1 speed speed of the body (only one speed per project)ENDSPEED end line for the definition of speed

SIDEWALL WIDTH w DEPTH d width of the channel and depth of the channelfor computations including sidewall effects

The picture displayed in figure 5.1 presents an example of input file for hsrdf module:

FILENAME w26

NBFREQUENCY 15NBHEADING 5NBSPEED 1

FREQUENCY TYPE 2WMIN 0.05WMAX 1.45WSTP 0.10

ENDFREQUENCY

HEADINGS TYPE 1180.0 225.0 270.0 315.0 360.0ENDHEADINGS

SPEEDS TYPE 01 0.0ENDSPEEDS

WATERDEPTH infinity

REFPOINT BODY 1 137.020 0.0 0.0REFWAVE 137.020 0.0

ENDFILE

Figure 5.1: Input file for hsrdf


5.2 Elimination of irregular frequenciesThe lowest irregular frequency for a parallelepiped is:

irr =gk/ tanh kT with k = pi

1/B2 + 1/L2 (5.1)

where (L,B,T) are length, width and draft of the box.

For a ship, the lowest irregular frequency is close to that estimated by above formula usingships length, width and draught.

For a body of arbitrary geometry, the lowest irregular frequency is larger than that for abox which can surround the body.

The irregular frequencies are eliminated in HydroStar by generating a mesh on the vesselswater-plane (that not necessarily covers all the water-plane area), and modifying the originalintegral equation by extending the singularity support to the internal water-plane.

The user has the possibility of changing the ratio between the panel size of the mesh andthe panel size of the water-plane by inputting a value for COEFZ0 in the hull mesh input filein order to get better accuracy of results for high frequency values, if desired (see fig 5.2).

Figure 5.2: Water-plane mesh


5.3 Encounter frequency approximationIn order to take into accound the forward speed, the so-called encounter-frequency approx-imation is implemented in HydroStar (module hsrdf) based on the use of the Green functionassociated to the encounter frequency.

The encounter frequency is defined as:

enc = [1 cos (V/g)] (5.2)

with wave frequency , heading and speed V .

In the following sea (|| < pi/2), can be close to zero. To avoid the singularity, specialtreatments are provided in hsmec (keyword ZEROENCFREQ). The boundary condition on shiphull is linearized over uniform flow.

5.4 Sidewall EffectsIn the version 6.0 of HydroStar, the user has the possibility of accounting for sidewall effects.This feature can be applied to verify the effects of the walls of a channel or of a wave tank onthe behaviour of body. Its known, for example, that some results from model tests performedat wave tanks exhibit some scattering comparing to the expected results in open sea condition.This can be explained by the reflections at the sidewalls of the tank. Its then worthwhile toperform numerical computations in order to obtain verify the adequacy of the wave tank for aspecified test or to limit the test duration in order to reduce the effects of wave reflections.

In the source panel method we use the Tank Green Function (TGF) which satisfies the lin-earized free surface conditions as well as the conditions at the tank bottom and walls. In factthe TGF may be written as a formal sum of Green Functions in open sea representing theinfinity images of the singularity with respect to the side walls.

G (M,M ) =

n=G0 (M,M n) (5.3)

where G0 (M,M n) is the open sea Green Function representing the potential at M due to thenth image of the source at M n.

However, the convergence of the direct computation of the infinite series is very slow. Amore efficient method consists to decompose the finite water depth TGF into two parts: afinite series of the open sea Green Functions and an asymptotic part which may be regarded asthe remaining terms of the infinite series and expressed by two single integrals whose kernels


decrease exponentially with the integral variable.

G =2N+1

n=2N1G0n +

n=N+1

G02n +G02n+1 +G02n +G02n1 (5.4)

The main advantage of the above decomposition is the rapid convergence of the asymptoticpart.

5.5 Diffraction and radiation computationAfter the preparation of the input file, the user is ready to start the computation by just typinghsrdf name file in HydroStar window:

Hstar>proj>hsrdf projrdf.don

The user has the possibility of running several times hsrdf in order to compute the wave diffrac-tion and radiation for additional frequencies that may be necessary just changing the extensionof results file in the input file and the definition of the wave frequencies. For example, fromlooking at the RAO files, the user may notice some complementary frequencies, e.g. on theresonance region, to perform a new run. Different runs of hsrdf can be combined at the inputfile for hsmec.

5.6 Radiation/Diffraction interpolation : HSpln moduleAs the Radiation/diffraction is the most time consuming part of the calculations, the frequencystep is not always as fine as desired. Instead of interpolating RAOs that sometimes presentsharp resonance, it is better to interpolate the radiation/diffraction results which are muchsmoother.

The following keywords shall be used in the input file for hspln execution:

FILENAME file name extension used in HSrdf calculationsFREQUENCY TYPE itype Wave frequencies. Same as for HSrdffrequency linesENDFREQUENCYINTERPOLTYPE LINEAR Linear interpolation

NATURAL Natural cubic spline (continuous second order derivates)OVERHAUSER Overhauser cubici spline (Also named Catmul-Rom)HERMITE Hermite cubic spline interpolation

FILENAME OUT extension o f the output fileENDFILE to end the hspln file


Several interpolation are available, the Overhauser spline is recommended. However, forparticular case where the hydrodynamic coefficients present sharp peaks, Hermite interpola-tion can be more robust. (The required derivatives are evaluated so that the resulting Hermitspline does not overshoot the original data.)

5.7 Radiation computation inside tanksWhen the tanks are included in the input file of hslec, the radiation problem inside the tankscan be solved. In HydroStar, the exterior problem (for the body) and the interior problem(for the tank) are solved separately using two different modules. For the exterior problem, themodule hsrdf is used, and for the problem inside the tank the module hstnk is used. The sameinput file described in item 5.1 is used for both modules.

After running hsrdf, the user needs to run hstnk by typing:

Hstar>proj>hstnk projrdf.don

The results obtained from hsrdf and hstnk will be combined when the motion computationwill be done.

Chapter 6

Motion Computation

The Newtons Second law was applied to describe the motions of floating bodies and thefollowing motion equation was derived and it:

([M ] + [MA])U + [B]U + [K]U = F (6.1)

where:

[M ] is the inertia matrix of the body; [MA] is the additional mass matrix coming from radiation problem solution; [B] is the damping matrix coming from the radiation problem solution and additional

damping defined by the user; [K] is the stiffness matrix coming from the hydrostatic properties of the body or additional

stiffness due to mooring system or liquid in tanks; [U ] is the motion vector of the body; [F ] is the excitation load of incident wave coming from the Froude-Krylov and diffraction

problem solution.

6.1 Input dataIn order to solve the equation above described, the user shall define the position of the centreof gravity, the inertia matrix, additional stiffness matrix and the additional damping matrix.

6.2 Input fileThe following keywords shall be used in the input file for hsmec execution:

61


.

FILENAME file name extension of file usedin hsrdf computations

MASS BODY no body, mass mass of the bodyGYRADIUS BODY no body, R44, R55, R66, R45, R46, R56 gyration radius of the

bodyCOGPOINT BODY no body, (XG, YG, ZG) centre of gravity of the

body in the mesh ref-erence

or

INERTIAL MATRIX TYPE itype BODY no body start line of inertialmatrix definition

Inertia linesENDINERTIAL MATRIX end line of inertial ma-

trix definition{

If itype = 0: the full inertia matrix shall be givenIf itype = 1: only the non zero values shall be given j, k,Mjk

ENDFILE end of the input file

The following keywords are optional:

REFPOINT BODY no body, xref , yref , zref reference point of computations(default=COG)

RHO fluid density(default=1025kg/m3)

GRAVITY g gravity acceleration(default=9.81m/s2)

REFWAVE xwav, ywav reference point of incoming waves(default=0;0)

REFLENGTH ref length reference length(default=1.0)

ZFSURFACE zfs coordinate of the freesurface in theuser reference system (see item 2.2)

ZEROENCFRQ no zero encf number of zero-encounter frequenciesif no zero encf =0: No treatmentif no zero encf =1: treatment in the range 0.1 < < 0.1if no zero encf =2: treatment in the range 0.2 < < 0.2

Chapter 6. Motion Computation 63

LINVISCOUSDAMPING no body, %B44crit linear roll viscous damping,in percentage ofcritical damping

DAMPING MATRIX TYPE itype BODY no body start line of linear dampingmatrix definition

Damping linesENDDAMPING MATRIX end line of linear damping

matrix definitionIf itype = 0: the full damping matrix shall be givenIf itype = 1: only the non zero values shall be given j, k, BjkIf itype = 2: only the non zero values shall be given j, k,%Bjk

QDAMPING MATRIX TYPE itype BODY no body start line of quadraticdamping matrix definition

Quadratic damping linesENDQDAMPING MATRIX end line of quadratic damp-

ing matrix definition{If itype = 0: the full quadratic damping matrix shall be givenIf itype = 1: only the non zero values shall be given j, k, BQjk

STIFFNESS MATRIX TYPE itype BODY no bodyi no bodyj start line of stiffness matrixdefinition

Stiffness linesENDSTIFFNESS MATRIX end line of stiffness matrix

definition{If itype = 0: the full stiffness matrix shall be givenIf itype = 1: only the non zero values shall be given j, k,Kjk

NOTANKS not to include tanks (in casetanks hstnk has been run)


WAVEAMPLITUDE value wave amp wave amplitude only for the calculation of thequadratic damping purpose (default =1.0)

ITMAX max iter maximum number of iterations for thequadratic damping linearization (default =1000)

CONVERGENCE ERR convergence criteria (default = 0.001)

The picture 6.1 presents an example of input file for hsmec module:

FILENAME w26

MASS BODY 1 1.13253E+08COGPOINT BODY 1 137.081 0.000 3.136GYRADIUS BODY 1 13.462 67.602 68.776 0.000 4.632 0.000

REFLENGTH 1.00RHO 1025.0REFWAVE 0.000 0.000

LINVISCOUSDAMPING 1 5.0 %

ENDFILE

Figure 6.1: Input file for hsmec

In case of single body the keyword BODY may be omitted. However, in case of multi-body itsnecessary to include it. If its not included all the values given are atributed to BODY 1 bydefault. Special attention should be paid to the stiffness matrices in case of multi-body, wherethe numbers of the two bodies have to be given after the keyword BODY.

IMPORTANT: In case of seakeeping-sloshing coupled analysis, differently from the previousversions where the mechanical properties are given in the input file should excluding the liquidin tanks, in version 6.0 the user must give the mechanical properties (mass, centre of gravityand gyration radii) including the liquid inside the tanks.

6.2.1 Centre of GravityThe longitudinal, transversal and vertical positions of the centre of gravity with respect to theorigin of the reference system must be given.

6.2.2 Gyration RadiusThe gyration radius in HydroStar should be always defined with respect to the centre of gravityof each body.


6.2.3 Inertia MatrixThe 6 x 6 inertia matrix can be given by the user. In this case, the shape of the matrix maybe arbitrary and its values shall be defined with respect to the reference point (if not given, bydefault its taken at the centre of gravity).

In case the user defines the mass of the body, gyration radius, centre of gravity and refer-ence point, the inertia matrix calculated by HydroStar has the following shape:

[M ] =

M 0 0 0 M.ZGC M.YGC0 M 0 M.ZGC 0 M.XGC0 0 M M.YGC M.XGC 00 M.ZGC M.YGC I44 I45 I46

M.ZGC 0 M.XGC I54 I55 I56M.YGC M.XGC 0 I64 I65 I66

where:

M is the mass of the body; XGC = XG XCal; YGC = YG YCal; ZGC = ZG ZCal;

with:

+ XG, YG and ZG being the position of the centre of gravity in the mesh reference;+ XCal, YCal and ZCal being the position of the calculation point.

I44 =M

[(y YCal)2 + (z ZCal)2

]dm = M

(R244 + Z2GC + Y 2GC

) I55 =

M

[(z ZCal)2 + (xXCal)2

]dm = M

(R255 + Z2GC +X2GC

) I66 =

M

[(xXCal)2 + (y YCal)2

]dm = M

(R266 +X2GC + Y 2GC

) I45 = I54 =

M

(xXCal) (y YCal) dm = M(R254 +XGC YGC

) I46 = I64 =

M

(xXCal) (z ZCal) dm = M(R264 +XGC ZGC

) I56 = I65 =

M

(y YCal) (z ZCal) dm = M(R256 + YGC ZGC

)


The user can input the full Inertia matrix or choose to input the following data:

The mass of the body: M ; The position of the centre of gravity: (XG, YG, ZG); The gyration radius: R44, R55, R66, R45, R46, R56

where:

+ Rii =

IiiM

with respect to the COG

+ Rij = sign(Iij)|Iij |M

with respect to the COG

6.2.4 Stiffness Matrix

The hydrostatic stiffness is computed by HydroStar. Nevertheless, an additionnal stiffness ma-trix may be added by the user, for example to take into account for mooring systems. The userhas the possibility of inputting the complete stiffness matrix, or only the non-zero terms.

In the case of a single body the matrix has the dimension 6x6. However in case of multi-body the full stiffness matrix has the size 6Nx6N, where N is the number of bodies. In orderto simplify the input of data, the matrix in case of multi-body is divided in NxN sub-matricesin the following way:

K BODY 1 1 K BODY 1 2 ... K BODY 1 NK BODY 2 1 K BODY 2 2 ... K BODY 2 N... ... ... ...K BODY N 1 K BODY N 2 ... K BODY N N

In the above matrix, the sub-matrices [K BODY i i] with (i= 1, .., N), represent the stiffness ofthe bodyi due to the motions of the body i itself. The sub-matrices [K BODY i j] represent thestiffness of the body i due to the motions of the body j. And finally the sub-matrices [K BODYj i] represent the stiffness of the body j due to the motions of the body i.

In summary, when specifying the stiffness matrix in case of multi-body, the user needs todefine two bodies numbers after the keyword BODY. In the case of single body this keywordcan be omitted as by default HydroStar assumes BODY 1.

As an example, in case there are two bodies connected to each other the user may definefour stiffness matrices as below:


STIFFNESS MATRIX TYPE 1 BODY 1 11 1 1.0E+042 2 1.0E+066 6 1.0E+10ENDSTIFFNESS MATRIX

STIFFNESS MATRIX TYPE 1 BODY 1 21 1 -1.0E+042 2 -1.0E+066 6 -1.0E+10ENDSTIFFNESS MATRIX

STIFFNESS MATRIX TYPE 1 BODY 2 11 1 -1.0E+042 2 -1.0E+066 6 -1.0E+10ENDSTIFFNESS MATRIX

STIFFNESS MATRIX TYPE 1 BODY 2 21 1 1.0E+042 2 1.0E+066 6 1.0E+10ENDSTIFFNESS MATRIX

6.2.5 Damping Matrix

The damping due to radiation is computed by HydroStar in the hsrdf module. However, inaddition to the radiation damping, there are other sources of damping acting on the floatingbodies such as the fluid viscosity and the mooring and risers systems damping. The effectsof viscosity on the hull and on the appendages on roll damping are generally higher than theradiation damping, a special paragraph below explain the different ways to take these effectsinto account. The additional damping can be inputted by the four following ways:

Linear damping in absolute values:The damping matrix is up-dated adding the damping values inputted.

Quadratic damping in absolute values:The quadratic damping is so called because it varies with the square of the responseamplitude. Knowing that the response amplitude depends on the quantity of damping,it can be deduced that the value of the quadratic damping is computed by iterativeprocedure. The quadratic damping is also very dependent on the wave amplitude and itseffect is more important at the resonance region.HydroStar then linearize the quadratic damping according to : BL = 83pi x BQ (where is the frequence and x the motion amplitude).


Linear damping in percentage of the critical damping:The absolute value of damping is calculated from the critical damping value and thedamping matrix is up-dated adding these values. Linear and quadratic damping with Ikeada, Tanaka, Himeno (ITH) formulation for roll

motion:The absolute values of damping are calculated from the geometry of the hull and of theappendages and the damping matrix is up-dated adding these values.

Roll Damping

As it is written above, the appendages are generally not modellized in HydroStar mesh. More-over, the fluid model used in HydroStar is the perfect flow model without viscosity. But viscosityand appendages increase the damping for roll motion in such an extent that it cant be neglicted.We suggest to use one of the following approximations to have a more realistic roll damping:

Linear damping in percentage of the critical damping is mostly used because it is certainlythe easiest way for ships and the one that need the less computation. We suggest theseapproximation for ships:

+ Tanker, Bulk Carriers: 4% - 8% of critical damping;+ LNG Carriers: 5% - 8% of critical damping;+ Containership 3% - 5% of critical damping.

Quadratic damping in absolute value for barges. Molin suggests:

+ BQ = 12 CD B4L

where:

- is the fluid density;

- B is the ship width;

- L is the ship length;

- CD is a coefficient from 0.04 to 0.1.

ITH formulation should be used when the user have any geometrical informations aboutthe appendages. The ITH formulation is a semi-empirical formula. It separates the severalsources of roll damping according to :

BT = BF +BE +BL +BW +BBKN +BBKH +BBKW +BSK

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