Ship Oscillation Simulation System Based on Direction Spectrum

(1)

Proceedings of the IEEE

International Conference on Automation and Logistics Shenvang, China August 2009

Ship Oscillation Simulation System

Based on Direction Spectrum

Ba Huang Jianwen Zhao Yanyu Su Shizhou Lu Shipping College, Harbin Institute of Technology

Weihai, Shandong Province, China 264209,

Email: Huangbo74l63.com

Abstract -Oscillating motion of ship makes a great impact on the safety of ocean shipping of LNG tank, so a simulation system is built to study the ship oscillation under different

conditions. We construct several groups of simulation

environment and an algorithm based on direction spectrum to describe ocean wave spectrum according to Seakeeping

theory, ship oscillation simulation system based on this

algorithm is built by VC+ and DirectX. The system could simulate the ship 's real-time movement under different sea conditions, and the simulation results are close to the ship 's

experimental data. It could provide strong technical support to study the LNG tank ship oscillation problems.

Index Termns -oscillation, simulation, direction spectrum, ship t. INTRODUCTION

Tank Container shipping is the main modes of transport for LNG, but how to ensure transportation safety is the key

question [I 2]

As the ship's oscillating motion makes the greatest impact on the pressure and liquid level changes of LNG in the tanker, therefore, it is very necessary to study

deeply into sorne problems of ship's oscillation.

The research about ship's oscillating motion is the study of ship Seakeeping, which means a ship's ability to navigate safely under a certain speed when oscillating , slamming,

stalling, green water and and water exiting in propeller cased by the swash of waves. The ship Seakeeping, like ship speed

and resistance , stability and subdivision should be considered

at the beginning of ship design as a main factor to determine principal dimensions, ship form and such elements to make

ship design the genuine integrated dynamic design'21. Existing ship oscillation simulation system mainly use wave spectrum

to describe random waves based on St.Denis and Pierson's frequency analysis method'3, the simulating of wave and ship's motion are calculated and generated image rendering

separately, which lead to the poor authenticity of the image. In order to solve this problem, we use direction spectrum to replace ocean wave spectrum to describe the random waves, it not only improves the accuracy of the results, but also makes

the movement of ship and waves more concert. As a result,

this system is more suited to the actual needs for the studying of oscillation problems of LNG tank container.

DeIft University of Technology

Ship HydromechafliCS Laboratory

Library

Mekelweg 2

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H. System simulation environment

Wind and ocean waves are the main affecting factors for

ship's oscillating motion.

The strong wind causes the ship yaw and sway and impacts ship pilot's observation of surrounding circumstances.

Different scale of wind makes different tent of impact on the

ship's motion. Some research works show that there are more

maritime traffic accidents when the wind is higher than 6 Beaufort-scale141.Even when the winds are of the same Beaufort-scale but the blow direction, the effects on

manipulation of ship are also different. It will be more obvious when the ship under the action of beam wind but less when the wind comes from other directions.

The waves impact ship's oscillating motion greatly. Ship

under wave disturbance may produce a variety of sport sway,

slamming, stalling and destroy the water propeller and even worse a capsize accident may happen under the action of a

much higher wave-scale.

The simulation environment constructed under the stormy wave environment is as Table I shows. In this system, we can

choose different ship speed, navigating course, wind speed and course to simulate under different actions of sea-conditions and navigations. The parameter range is shown in

table I.

Table 1 Sinmlation environment Parameters

Ill. Calculation of simulation system

The wave described by direction spectrum is decomposed

into many wave components from frequency domain and

time-domain, then calculate the values of frequency domain of

oscillating motion cased by every wave component and then

convert them into time-domain values according to frequency Nurn Ship Speed (knot) Ship Course (deg) Wind Speed (mis) Wind Direction (deg) 0 17.5 0 2 0 1 16 45 2.5 0 2 15.5 90 5 0 3 14 30 7 0 4 IS 50 8 0 5 13 45 10 0 6 II 35 13 0 7 10 35 14 0 8 9 45 16 0 9 8 80 18 0 Range 0-20 0-90 0-30 0-180

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spectrum analysis theory61, finally superpose those results to obtain the data of ship's oscillating motion according to linear superposition hypothesis.

1. Mathematical model of wave

Considering energy's distribution in wave's interior, we

decompose wave from frequency and time domain.

The relation between direction spectrum S° (w,) and wave spectrum S(co) is given by

S(w)= $SD(w,%)d%

SD (w,)

= S(w)D(w,)

(2)

Where w is the wave's frequency (hz), % is the wave angle is the orientation distribution function.

We choose P-M spectrum and ITTC orientation distribution function to obtain the direction spectrum from (2). The formula of P-M spectrum is:

A

SrM (w) = i-exp

in which A= 8.11x103g2 ,g is acceleration of

gravity(mls2);B=O.74g41 , is the wind speed I 95m

above the sea-surface (mis)

The formula of ITTC orientation distribution function is as follows:

2COSg

r L22 ₍₄₎

in which

= X -

CeatralWove , it is the angle of the wav&s direction % and the centerwave z

From (2) (3)and(4), we obtain the formula of spectrum based on P-M spectrum and ITTC orientation distribution

function as(5)shows:

2 Mathematical model of ship's oscillating motion

(I)

B

(3)

In (5), wave angle a uses equal angle method to divide, and

the number of division depends on the actual needs;

frequency w also uses equal angle method to divide based on

Table 2171.Then, the wave components are obtained on different

frequency and wave angles by (5).

Table 2 Wave's freuencv range and dccomosition scheme

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It is the encounter wave causes the ship's oscillating motion, and the motion also affects the encounter wave. Therefore we should first transform the actual wave into the encounter wave and then make it the external excitation to obtain the data of oscillating motion. The method is as follows: firstly obtain the encounter frequency and encounter wave spectrum by studying the relation between actual wave and encounter wave, then get the value of frequency and

time-domain by response amplitude operator according to linear

superposition theory.

The mathematical relation between ship's encounter frequency a and natural frequency w is as follows:

w p,.5, cosji

w=w

(6)

g

Where /ship is the average speed of ship(mls); ,u is the

encounter angle(deg), p =x x,,, the angle of wave direction

and ship direction; We can get (7 ) from (6):

dw 2C0/Juh,P

=1

cosii

dw

The relation between wave spectrumS(w) and encounter

wave spectrum S(w) is described as follows: $S(w)dw= JS(w)dw,,

o O

From (7) and (8), we can obtain S (we) as (9) shows:

S(w) S(w)

dw I

dw,. g

The relation between ship motion and wave height versus regular wave frequency is commonly called Response

Amplitude Operators(RAO), which is made up of amplitude frequency function RAO( Û) e. /11 .

//

ship )I and

phase-frequency function Ç) (We, /1. /1 ship) as (10) shows RA O (w,, , P' Puhip ) =

RAO (wr,p,pohip )(We,P,Pnhip)

(10)

The RAO depends on the geometry of the hull and load

conditions of the vessel as well as its speed and direction with

respect of the waves, and it is determined using strip theory

computations in which the forces and moments are integrated

over the wetted surface of the hull'9"0t.

We obtain the function of ship's motion by encounter wave spectrum and RAO, and then calculate the frequency

domain solution of the ships oscillation.

According to linear hypothesis of the response to the ship

motion and in accordance with the above-mentioned system function, the oscillation spectrum of motion at a certain sea

condition can be calculated by the following formula

S, (ii,

501) = _5'i,.i 'P1' Pu0ip) (11) ¡=0 j=O a (7) Wave Scale Wind Speed (mis) max (Radis) Frequency Range ( Hz) Angular interval Division Amount 1 <5.5 >1.57 1.2-6.0 0.2 24 2 5.5-8 1.57-1.07 0.6-0.4 0.2 17 3 8-1 1.5 1.07-0.71 0.4-2.5 0.! 21 4 11.5-14 0.71-0.62 (1.4-1.8 II).! 22 5 14-17 0.62.-0.51 0.3-1.4 0.05 20 6 >17 <0.5! 0.2-1.2 0.005 20 5D _{(w,a') =} 2COS'ca O A (B [ if 'rl L5TJ I if'r ael--,-_{L 22} (5)

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'z

t>T11 =J)sin(Û),t+3+)

¿=0 j=O ¿=0 j=O

7lj).J2XS,, (Û,p,,,u0,)xAÛ1xAp

Where 7 _is _{the displacement in Direction} _i _is _the

amplitude of Number (i,

j)

wave component in Direction a, is the encounter frequency of Number (i,

j)

wave

component in Direction is the Random phase of Number

(i, j)

wave component in Direction is the Response amplitude operator of Number (i, j) wave component in

Direction

IV. Implementation of ship oscillation simulation system System module division

The simulation system is made up of calculation module and three-dimensional real-time simulation module. The

general module division is as Figure 1 shows.

Implementation of system module

Calculation module gives the simulation data of ship's

motion that the ship simulation module will use from the data of wave and ship inputted by user. The process of computation

follows the steps of pre-processing, frequency calculating,

time-domain calculating and simulation calculating.

The pre-processing computation is to crystallize wave's decomposition approach based on P-M spectrum and ITTC

orientation distribution function according to Table 2.

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module

J J I

t

'e

Fig. 2 Simulation of wave

Simulation module

u

Figure 1 System module division

The frequency and time-domain computations are to calculate frequency and time-domain values of ship's oscillating motion by using (Il )==( 15). Simulation computation is to calculate and

save the data needed by three-dimensional real-time simulation module by using the calculating results of the other three modules.

Three-dimensional real-time simulation module is divided

into wave simulation module and ship simulation module. Wave simulation module is divided into sea-surface module and grid module. The height of arbitrary point in the wave height field of sea-surface module is obtained by Gerstner model. The grid module is constructed by grip projection technique,and then we use GPU to rendering. The figure 2

shows the simulation of wavelet, medium wave and strong

wave.

Ship simulation module is made up of ship calculation model and ship three-dimensional model. Ship calculation

model realizes the hull model by importing the table of offset

to Fastship and gets the RAO data by using grip projection

technique.

Then we can get the simulation model by

importing the hull model to

Maya to

construct the

superstructure and save the results as X-file format which

DirectX9 uses, Figure 3 shows a three-dimensional model of a

tanker.

r

Fig. 3 Fluge tanker model

V. Analysis of simulation results

The system could simulate ship's real-time response. Figure 4 shows the three-dimensional real-time simulation.

The three columns show the ship's motion under the actions of

wavelet, moderate sea and strong wave. Each line shows the comparison of sea colour, light intensity and location in the

three sea-conditions mentioned above.

s5, 'Pi, Pc;,q,)

(12)

=

) s° (p,,w)M

Phase5,(,u _I1uhip)

= Phase,7,_{(z 'Zsiup'P,5,p) = 7(II,P,h,p)} (13)

(Il) shows Number i motion's spectrum value of ship's

oscillating motion is the phase value of wave components and

ship's motion on condition that the encounter angle is which means the center wave's direction is and the ship's motion direction is ,' _,,,,.

shows the spectrum value of ship's oscillating motion

cased by Number j frequency's wave component in Number i wave. The M in the formula is a factor, its value is i when

the calculating degree of freedom is linear displacement, or h

when the calculating degree of freedom is angular displacement, where his the number of waves.

shows the phase of ship's oscillating motion of

Number i is the value of phase-frequency function determined by encounter angle

, ¡nain and ship speed p ship

When calculating the time-domain value of ship's oscillating motion, we use trigonometric functions to describe

the wave components' motion and use component motion to

describe ship's oscillating motion based on linear superposition theory. The formula is given by

model system lave Simulation model Ship o no

(4)

L 5

o.

-0.

-L 5

Figure 4 Figure of three-dimensional real-time simulation In order to check the system's correctness, China International Marine Containers Co. has made navigating test, the results show that simulation matches with test. we take the tanker model under the action of 5-6 level north-easterly wind and I 5m waves environment to simulating. Then compare the

computation results with the test data to verif' the feasibility of the system. By simulating and calculating, we obtain the

first 65 seconds' data about the ship's roll and pitch moment as Figure 5 and 7 shows, Figure 6and 8 shows the experimental

data.

Simulation Roll deg s)

1 11 21 31 41 51 Sl II 21 31 41 51 61

Fig. 5 Rolling simulation data Fig. 6 Rolling experimental data

Siau1atian'itci (dei'- s) 1.9 0.6 0.3 i i: ¿1 31 41 51 61 39 06 03 C -0. 3 -0. 6 0. 9 t J. b o -o. E Roll (deg - s) Pitch (deg - s) lI 21 31 41 51 6

Fig. 7 Pitching simulation data Fig. 8 Pitching experimental data Contrast Figure 5 and Figure 6, Figure 7 and Figure 8, we know that the cycle of roll to the system and the experimental data are both about 20 seconds, and the amplitude both focus

on 0-1 deg, the simulation result is about 1.2 times higher than experimental data; the cycle of pitch to the system and the experimental data are both about 00 seconds, and the amplitude both focus on 0-0.3 deg, the simulation result is

about I .2 times higher than experimental data. Vt. Conclusion

In this paper, a ship oscillation simulation method based

on directional spectrum is constructed. This method could simulate the sea environment and the real-time response of

various ships under different ocean conditions. a ship's virtual

model is established to simulate its dynamic response under

different sea conditions. Compare the simulation results with

the experimental data shows that the dynamic response is

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synchronized, which validates the effectiveness of the method

and it could be used for studying the oscillation problem of

LNG tank container ship.

Acknowledgement

This work is supported by High Technology Research

and Development of China #2006AA040 103. Reference

[I] Jianhua Peng. Discussion on safety of water transportation of LNG tank container. Word Shiping, 2007, 30(3):27-28 Jide Li. Ship Seakeeping. Harbin Institute of Marine

Engineering Press. 1992:5-6

Wei Tao,Wenhua Zhao,Yuanzhen Zhao. Ship's

MotionSimulation in Virtual Reality. China Ship Research. 2006. 1(2): 77-79

Zheping Shao. Research on Assessment Models of Maritime Traffic Safety And Simulation APPlieations.2000. 21-22, 44-46

S. Denis, W. J. Pierson. On the motion of ships in confused seas. Trans SNAME. 1953,61:71-77

Jie Liu ' Beiji Zou ' Jieqiong Zhou, Yue Zhu. Modeling

Gerstner Waves Based On the Ocean Wave

Spectrum.COMPUTER ENG[NEERING & SCIENCE. 2006, 28(2):41.-44

P. Tristan, M. Blanke. Simulation of Ship Motion in Seaway. Technical Report EE02037. 1996:52-55

T. F. Ogilvie, E. O. Tuck. A rational strip theory of ship

motions. The Univ.of Michigan. 1969, 13:33-39

N. Salvesen, E. O. Tuck and O. Faltinsen. Ship Motions and sea loads.Trans SNAME. 1970, 78:259-287

S. Haverre, T. Moan. On Some Uncertainties Related to Short Term Stochastic Modelling of Oceanwaves. In: Probabilistic Offshore Mechanics, Progress in Engineering Science. CML Publications Ltd. 1985:59-64