03 Wadam Standard

DNV SoftwareSesam User CourseGeneral wave load analysis

Revised: August 22, 2012

© Det Norske Veritas AS. All rights reserved.

Wave Analysis by Diffraction And Morison theory

Computation of

wave loads and

global response

Slide 2


Diffraction & radiation theory

� Viscous effects neglected

� Distortion of waves due to presence of structure included

� Waves created by the motion of the structure included

� Linear theory

� Structural part with dimensions comparable to wave length (large volume part)

Slide 3


The problem to be solved

Moving bodyIncoming wave

Radiated and diffracted wave

Equations:

Conservation of mass => field equations inside fluid

Conservation of momentum => Equations of motion for body

Boundary conditions

Basic assumption: Inviscid fluid

Slide 4


Continuity equation (conservation of mass)

General equation: vdt

D r•−∇=ρρ1

00 =•∇⇒=⇒ vdt

D rρAssumption 1: Incompressible fluid

Assumption 2: Irrotational motion ϕ∇=⇒=×∇⇒ vvrr

0

Assumptions 1 and 2 give the following field equation in the fluid domain:

( ) 0,,,2 =∇ tzyxϕ

(Velocity potential)

Slide 5


Boundary conditions

� At sea bed: 0=∂∂=

nvn

ϕ

Iϕϕ =

(zero normal velocity)

� At infinity: (no disturbance of incoming wave)

� At free surface:

� Kinematic boundary condition: A water particle in the free surface will remain in the free surface

� Dynamic boundary condition: Atmospheric pressure

� Can be set to zero since a constant pressure give no force on a body

� On vessel: 0==∂∂

nVn

ϕ(normal velocity in fluid equals normal velocity of body)

Slide 6


Linear theory

� Assuming that the wave amplitude is “small”

� Expanding all conditions on free surface around mean sea level and keep only terms proportional to the wave amplitude

� Motion of structure is of the same order as the wave amplitude

� Expanding all conditions on structure around mean position and keep only terms proportional to the vessel motion

⇒ Computational grid (panel model) will be the same at all times

Slide 7


Linear theory - top view

Amplitude: 3m, direction 135°

Slide 8


Linear theory - view from below


Slide 9


Non-linear theory - view from below


Slide 10


Morison theory

� Viscous effects included

� Empirical formula

uuDCdt

duC

DF dm ρπρ

21

4

2

+=

Structural parts with dimensions much smaller than wave length (small-volume part)

Slide 11


Drag linearization methods

� Linearizing the non-linear drag force:

� Regular wave linearization (iteration process)- Find urel as the local relative velocity in each harmonic wave- Wave amplitude must be given

� Stochastic linearization (iteration process)- Find local urel from a wave spectrum- (Short crested or) long crested

� Give urel as a global constant (no iteration)

)(21

21

Bwreldd uuuDCuuDC −≈ ρρ

Excitation

Damping

Slide 12


Xtract in SESAM Overview

INTEGRATEDPROGRAMPACKAGES

SESAM INTERFACE FILE

PO

STP

RO

CE

SSIN

G

Xtract

presentation& animation

of results

Framework

framedesign

Stofat

shell/platefatigue

Profast

probabilisticfatigue andinspection

Cutres

presentationof sectional

results

Platework

platedesign

Concode

concrete designST

RU

CT

UR

AL

Manager

EN

VIR

ON

ME

NT

AL

Installjac

launching of jackets

Waveship

wave loadson ships

Wajac

wave loads on framestructures

Wasim

3D wave loadson vessels

PR

EP

RO

CE

SSIN

GA

SSO

CIA

TE

D

Proban

probabilisticrisk and

sensitivity

Workflow

Simo

marineoperations

Preframe

framestructures

Patran-Pre

general structures

Presel

super-elementassembly

Submod

sub-modelling

Prefem

general structures

Wadam

wave loadson generalstructures

Splice

structure-pile-soil

interaction

Usfos

progressivecollapse

Mimosa

mooring analysis

Riflex

non-linearriser

Sestra

linearstatics anddynamics

Postresp

presentationof statistical

response

Genie

conceptual modeller including:Wajac, Sestra, Splice, Framework

DeepC

deep water mooring analysisincluding: Simo, Riflex

FPSO

programs needed for FPSO designintegrated in Workflow

Xtractpresentation& animation

of results

Slide 13


Procedure for hydrodynamic analysis

HydroD

Mass Model(Patran-Pre, GeniE)

Panel Model(Patran-Pre, GeniE)

(Presel)Model of panel & mass model

Analysis control parameters

Seastate Transfer function Response

Postresp - short term

Scatter diagramLong term response

Postresp - long term

Output from Postresp:• Long term statistics• Display response variables• Combine response variables• Display response spectra

Wadam

Load transfer to structural analysis:• Inertia load• Wave pressure

Slide 14


Wadam input

Preprocessor(GeniE, Patran-Pre)

Panel ModelMorison Model Structural Model Mass Model

Presel

Hydro Model

Wadam

Environment

Slide 15


Panel model

� For the large-volume part of the structure

� Created by GeniE, Patran-Pre, Presel

� Shell or solid elements

� Single superelement or hierarchy of superelements

� External wet surface identified by the Wet Surface property in GeniE or Hydro load in Patran-Pre. This must be assigned to load case number 1.

� No, one or two symmetry-planes can be used

� Arbitrary position of origin

� Maximum 15000 panels

Slide 16


Adjustment of panel model to actual wet surface

This adjustment is done automatically in Wadam by adjustment of those panels that intersect the free surface

Warning: For load transfer the structural mesh should not haveelements intersecting the free surface

Slide 17


Morison model

� Used for the small-volume part of the structure

� Created by GeniE or Patran-Pre

� 2-node beam elements

� One single first level superelement

� No symmetry planes

� Defined by assigning hydrodynamic properties in HydroD

Slide 18


Reference frame for Wadamoutput

� Motions and forces are by default referred to Wadam’s internal frame of reference.- The motion reference point can be user specified, from Wadam version 8.2- Motion directions are in the global system

- Heave is motion vertical to the free surface

� In this system the mean free surface is identical to the xy-plane.

Slide 19


Hydro models in Wadam

Hydro model

Panel model Composite modelMorison model Dual model

A dual model is only needed for load transfer to a beam

structural model

Slide 20


Mass model

� Global mass data- Given in HydroD (Prewad)

- Centre of gravity, radii of gyration, products of inertia, total mass- or- Mass matrix

- Sufficient for computation of rigid body motion and pressure distribution

� Given by a superelement model- This can be the panel model, the structural model, the Morison model or a

separate model- Needed for computation of sectional loads

� Alternatively the mass may be given by a point mass file

Slide 21


Definition of waves

� Incoming wave defined as:

))sincos(cos(),,( ββωη kykxtAtyx +−=

Akω

Wave amplitudeWave number = 2π/Wave lengthAngular frequency = 2π/Wave period

β Wave direction (“going to” direction)

Input to Wadam:

Wave direction +

Wave length or Wave period or Angular frequency

β

X

Y

Slide 22


Wadam output

� Listing file:- Contents determined by PRINT-SWITCH- Datacheck + normal output- Can be VERY large with high print switch

� Loads Interface Files (L*.FEM)- Loads transferred to structural analysis in Sestra- Load cases produced must be accounted for in Presel load

combination (need not be done prior to Wadam run)

� S-file (S*.FEM) - part of Sestra input file- Correspondence between load cases and wave directions/frequencies- Essential for spectral fatigue analysis in Stofat / Framework

(Optional for a non-fatigue analysis)- Created when the first load case no. is 1

Global response

& Load transfer

Load transfer

Slide 23


Wadam output – listing file

� The list of contents is useful and is also showing what is printed for different settings of the print switch

Slide 24


Wadam output

� Rigid body motion RAO

� Mass, added mass, damping and restoring matrices

� Excitation forces

� Mean drift force

� Wave elevation at specified points

� Wave kinematics at specified points

� Pressure RAO on selected panels

� Global loads RAO (sectional loads)

Results Interface File - the G-SIF or G-SIN file(for Mimosa, DeepC, Postresp, Xtract)

Optional

Slide 25


Response Amplitude Operators (RAOs)

� Response per unit wave amplitude as function of wave period and heading

Input: )cos( tω Output: )),(cos(),( βωδωβω +tT

Wadam

Transfer functionSeastate Response

Postresp

Slide 26


Complex variables

� The RAO (Transfer function) is most conveniently treated as a complex variable

Input:

Output:

CRi iTTeTH +== ),(),(),( βωδβωβω

)Re()cos( tiet ωω =

Positive phase angle, δ, means that the response peakoccurs before the wave crest reaches the origin

)),(Re( tieH ωβω

The phase angle is model dependent, only relative phase angles have a physical meaning

Slide 27


Example: Heave RAO

A typical RAO fora semi-submersible

Slide 28


Example: Heave RAO

A typical RAO fora ship

Slide 29


Roll damping methods in Wadam

1. Use an external damping matrix

2. Use the roll damping model in Wadam (ships only)- Requires an iteration since maximum roll angle is a parameter

If maximum roll angle is from short term statistics automatic iteration can be performed- Involves definition of a 2D strip model- One symmetry plane (XZ plane) must be used

3. Use the quadratic roll-damping coefficient- Requires stochastic iteration

4. Use a composite model

Only option 3 allows for load transfer of the roll-damping force

Slide 30


Typical approach

1. Use the roll damping model in the global analysis

2. Use a composite model in the load transfer. Damping coefficients are tuned so that the resulting damping matrix is the same as in the global analysis

Slide 31


Waves in shallow water

� Validity of result is limited by the validity of the wave theory (Airy) which is used in Wadam and Wasim. The limit depends on the wave lengths studied and the size of the waves.

� “Tentative minimum water depth” (the smaller value requires small amplitudes)- 40-70m for T=15s (wave length 340m – “infinite depth” = 170m)- 20-40m for T=10s (wave length 150m – “infinite depth” = 75m)- 5-10m for T=5s (wave length 38m – “infinite depth” = 20m)

� The requirement on water depth increases linearly with wave length for constant wave steepness (steepness is wave height/wave length).

� The requirement on water depth increases linearly with wave steepness for constant wave length.

� Wave length increases with wave period squared.

Slide 32


Wave theories and shallow waterExample 1:

T=15s, d= 22m / 45m / 220m

Linear: H < 0.9m / 1.25m / 2.25m

Stokes: H < 6m / 22.5m / 68m

Breaking: H > 13.5m / 34m / 68m

Example 3:

T=5s, d=2.5m / 5m / 25m

Linear: H < 0.1m / 0.15m / 0.25m

Stokes: H < 0.65m / 4m / 7.5m

Breaking: H> 1.5m / 4m / 7.5m

Example 2:

T=10s, d= 10m / 20m / 100m

Linear: H < 0.35m / 0.55m / 1.0m

Stokes: H < 2.5m / 10m / 30m

Breaking: H > 6m / 15m / 30m

In practice the linear limits can be pushed quite a lot

Slide 33


Airy wave vs. Stokes 5th order wave

100 105 110 115 120 125 130 135 140 145 150

-5-4

-3-2

-10

12

34

56

7

Time

Incoming wave - WasimActivity_h10_lin_U0 Incoming wave - WasimActivity_h10_stokes_U0

100 105 110 115 120 125 130 135 140 145 150

-1-0

.8-0

.6-0

.4-0

.20

0.2

0.4

0.6

0.8

100 105 110 115 120 125 130 135 140 145 150

-2e+

009

02e

+00

94e

+00

9

Wave height: 10mWave period: 17.27sWater depth: 30m

Wave elevation

Heave

Midship Vertical Bending

Containership

Slide 34


Running Wadam� Start from the Activity Monitor

� May include both Stability analyses and Wasim analyses

� Use of HydroD is described in a separate presentation in the training course

Possible to execute multiple activities (Threads) in parallel

Slide 35


Wadam additional features

� “Time domain” (deterministic) output

Extensions (additional licences):

� Multibody computations

� Second-order response and excitation forces

� Wave Drift Damping

Slide 36


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Skide 37

Documents

03 Wadam Standard