Numerical Modelling of Marine

Structure Behaviours in Steep

Waves

Q.W. Ma and S. Yan

City, University of London

The 136 meter long cargo vessel Mustafa

Kan sank in the Mediterrean Sea. The

Mustafa Kan ….. suffered water ingress in

the engine room from Shipwreck Log. Sept.

2016.

North Sea oil rig battered by waves due to

massive storm swells over the North Sea on

January 10 2015 (BBC News put on YouTube)

One person died and two other were injured

after a large wave hit a semi-submersible

drilling rig operating in the North Sea on 30

Dec 15 from gCaptain

Introduction - Some Recent Marine Incidents

Introduction – question to be asked What went wrong, causing the incidents?

Waves used for design are different from the real waves

Not real spectrum (statistics or not resolved)

Symmetrical design wave

Linear and/or steady survival wave

Current just changing encountered frequency

No effects of wind on waves

Not aware the waves coming in a short time

and so on

Simplification of Wave-Structure interaction

Invariant wetted body surface

Ignoring viscosity and aeration

Rigid body

Forward speed modelled as current in modelling test

and so on

Introduction – how to answer question

Waves:

Modelling real waves in a sea state in a large scale

Modelling full wave-current interaction

Modelling the seabed effects on waves and spectrum

Predicting the large waves coming in a short period

and so on

How to rectify difference and simplification said above?

Wave-Structure interaction

Modelling fully nonlinear wave-structure interaction (WSI)

Modelling Wave breaking effects on WSI

Considering deformable body

and so on

Bottleneck: Inefficiency and incapacity of existing methods

Numerical Modelling Outline

Next Generation

Numerical Modelling Methods

FNPT NS

Hybrid

QALE-FEM ESBI/

Hybrid

ESBI

MLPG_R OpenFOAM

FEM-MLPG

MLPG-SPH

FEM-CIP

FEM-StarCD

FEM-

OpenFOAM

Fully nonlinear

potential theory

Fully nonlinear

viscous theory

(Navier-Stokes

eq.)

IBM

IBM

Solitary wave on a 3D symm. seabed

Individual overturning waves by QALE-FEM

11 11.5 12 12.5 13 13.50.8

1

1.2

1.4

1.6

1.8

z

x-x0

y=0

y=0.5

y=0.8

y=1.1

Profiles at 9.16

Solitary waves over non-symm. Bed

ccb sykhxxZ )(sec)( 20

Seabed geometry may

lead to very different

overturning waves

Yan, S, and Ma, Q.W. (2010) ‘QALE-FEM for modelling 3D overturning waves’, International Journal for Numerical Methods in Fluids, Vol. 63, pp.743 – 768.

Directional and crossing waves by QALE-FEM

Low pass filtered 0.034Hz

Draupner wave (recorded in the

North Sea on 1st, January, 1995)

1200 Crossing-sea

result is closer to the

features of measured

data than the

following-sea result

Adcock, T., Taylor, P., Yan, S., Ma, Q.W., Janssen, P.A.E.M. (2011) ‘Did the Draupner wave occur in a crossing sea?’,

Proceedings of the Royal Society A, Vol. 467, pp. 3004-3021 (doi:10.1098/rspa.2011.0212).

Current effects on waves by QALE-FEM Focusing waves: N=32, xf = 10, τf = 125, ωmin = 0.8683; ωmax = 1.8825; Af

ranging from 0.002 to 0.1488; Current velocity ranges from -0.25cg to 0.25cg

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

1

1.2

1.4

1.6

1.8

Ucx

/cg

* m

ax/A

f

Af=0.1488

Af=0.128

Af=0.1114

Af=0.074

Af=0.037

Af=0.002

Opposite current

effects waves

significantly, but

depends on the

wave magnitude

For small focusing waves, the stronger current makes the wave steeper but

not significant.

For larger focusing waves, the stronger current may make the wave smaller.

Large scale simulation of random waves by

Hybrid ESBI Method A rogue wave of 2𝐻𝑠, (kH)s=0.05,

based on Wallops spectrum ), 16𝑚𝑖𝑛

for the simulation of 1000T0 on a

workstation (3h real time and 20km if

T0 is 10s)

4 rogue waves in random waves

3.2h for simulating 32 x 32 L0

and 100 T0 ( 10X10 km2 and

23m real time if T0 is 14s)

It is possible to simulate the

case up to 1000 T0 using more

powerful workstation available

today overnight.

Wang, JH, Ma, Q.W. and S. Yan (2016), ‘A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale’, Journal of

Computational Physics 313: 279–309.

Breaking waves by hybrid MLPG_R coupling with potential model -05

Some results

Total (in hrs)

IMLPG_R 8.27

Hybrid 1.44

Focusing waves

Overturning waves

Overtopping

Sriram, Ma and Schlurmann, ‘A Hybrid Method for Modelling Two Dimensional Non-breaking and Breaking Water Waves’, Journal of Computational Physics

272 (2014), 429–454.

FPSO in shallow water by QALE-FEM

15 20 25 30

-0.1

-0.05

0

0.05

0.1

heave f

orc

e/a

recorded heave force 3rd approximation difference

(b)

Comparison of recorded heave force and the

3rd-order approximation for (b) kd=0.94 (ka =

0. 1254, λ =0.833)

Fig.15 Ratio of the second-order

harmonic amplitude of heave force to

that of the first order

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

k/D

b s

pectr

a

bow

stern

Spectra of relative run-up recorded at the

bow and stern of the FPSO (ka = 0.084,

kd=0.63)

Nonlinearity play important role and 2nd components can be significant Yan, S., Ma, Q.W., Lu, Jinshu, Chen, Shuling, 2010 ‘Fully Nonlinear Analysis on Responses of a Moored FPSO to Waves in Shallow Water’, Proceedings

of ISOPE 2010, ISBN 978-1–880653–77-7, Vol. 1., pp. 501-507

Wigley Hull moving in waves by QALE-FEM

Heave R AO (head s ea, F n=0.2)

0

0.5

1

1.5

0 0.5 1 1.5 2 2.5 3

λ/L

He

av

e /

a

E UT(K ashiwagi,2000)

NS M(K ashiwagi,2000)

E xperiment(K ashiwagi,2000)

BE M(Tanizawa,2001)

QALE -F E M

P itc hR AO (head s ea, F n=0.2)

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3

λ/L

Pit

ch

/ka

E UT(K ashiwagi,2000)

NS M(K ashiwagi,2000)

E xperiment(K ashiwagi,2000)

BE M(Tanizawa,2001)

QALE -F E M

Length (L): 2m; Breadth: 0.3m and Draft: 0.125m; Fn=0.2

Computational results are very similar to the experimental results

Two ways (Frequency by frequency and random waves) of computing

RAOs give similar results what waves are not large

0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

/L

Pitch R

AO

JONSWAP Spectrum(1.8-2.9)

Single frequency (transient test)

Irregular waves modelling

Moving cylinder in focusing waves by QALE-

FEM Focusing waves: fl = 0.34 Hz to fu = 1.02 Hz. Ga = 0.002 for all 32 components; Cylinder moves towards the wave paddle with speed of 0.25m/s

67 67.2 67.4 67.6 67.8 68 68.2 68.4 68.6 68.8 690

5

10

15

20

25

30

35

40

time(s)

pre

ssure

(100P

a)

Exp

QALE-FEM 28.5cm below MWL

8.5cm below MWL

1.5cm above MWL

60 62 64 66 68 70 72 74 76 78 80

-0.1

-0.05

0

0.05

0.1

time(s)

(

m)

(a)WP6 in line with cylinder

Exp

QALE-FEM

Pressure at three positions

Wave elevation at a point in line with cylinder

P2

P3

P4

Acceptable agreement between the QALE-FEM prediction and the experimental data of the pressure recorded on the cylinder surface and of wave elevation

Yan, S., Ma, Q.W., Sriram, V., Qian, L., Ferrer, P.J.M., Schlurmann, T. (2015), ‘Numerical and Experimental Studies of Moving Cylinder in Uni-directional

Focusing Waves’, Proceedings of ISOPE 2015, Vol. 3 (ISBN 978-1-880653-89-0).

2 Wigley Hulls in Oblique Waves by QALE-FEM

Wavemaker: ω√(d/g)=1.7691, a/d=0.03

Numerical Tank: L/d=15; B/d=6

Distance: 1.5

Motion of small body

is affected by the

larger one

Ma, Q.W., and Yan, S. (2009) ‘QALE-FEM for Numerical

Modelling of Nonlinear Interaction between 3D Moored

Floating Bodies and Steep Waves’, International Journal for

Numerical Methods in Engineering, Vol. 78, pp. 713-756

2 structures in oblique waves by QALE-FEM

0 1 2 3 4 5 6 7 80

0.02

0.04

0.06

heave f

orc

e s

pectr

um

/a

a=0.03

a=0.02

a=0.002

0 1 2 3 4 5 6 7 80

0.02

0.04

0.06

sw

ay f

orc

e s

pectr

um

/a

a=0.03

a=0.02

a=0.002

2nd order > 1st order Nonlinear

components

increase

Load on Barge 1 (smaller) in the cases with different wave

amplitudes ( 30o incident angle, Bg=0.15, ω=1.676)

0 1 2 3 4 50

0.1

0.2

roll

spectr

um

/a

with Barge 2

Without Barge 2

Roll spectra of Barge 1 in beam sea (a=0.02, Bg=0.15, Beam Sea, ω=2.167)

Some mode can be enlarged by

other barge

Yan, S. and Ma, Q.W., Cheng, X. (2011) ‘Fully Nonlinear Hydrodynamic Interaction between Two 3D Floating Structures in Close Proximity’,

International Journal of Offshore and Polar Engineering, Vol. 21, No. 2, pp. 1–8.

Violent wave impact on elastic structures by

MLPG_R method Wave impact on a 2D plate

Deflection of plate largely

similar to experimental data

Deflection of plate makes

waves more complicated

Sriram, V and Ma, Q.W. (2012) ‘Improved MLPG_R method for simulating 2D

interaction between violent waves and elastic structures’, Journal of Computational

Physics, 231 (2012), pp. 7650–7670

Overturning Wave impact on a monopole of

OWE by MLPR_R

12 12.5 13 13.5 14 14.50

0.5

1

Pre

ssure

Point 1

Point 2

Second peak at Point 1 is larger

Point 1 and Point 2, on the front side of the cylinder are assigned to record

pressure; they are 0.1 and 0.3 above the mean water level (MWL).

10 10.5 11 11.5 12 12.5 13 13.5 14 14.50

0.5

1

Pre

ssure

Location A

Location B

Location C

wavemaker

er

1:10

MWL

A

B d

5d 1d 0.5d 2.4d

1d

1.1d

C

Pressure history shape

different for different positions

2-phase modelling of ship section impact

Liang Yang, Hao Yang, Shiqiang Yan and Qingwei Ma (2016) "Numerical Investigation of Water Entry Problems Using IBM Method“, IJOPE Paper No. JC-687

0.2 0.21 0.22 0.23 0.24

0

2

4

6

8

10

12

time(s)

Pre

ssure

(kP

a)

(e)P3

0.2 0.21 0.22 0.23 0.24

0

5

10

15

20

25

time(s)

forc

e(N

)(f)F3

IBM

OpenFOAM

Experiment

• IBM results agree well with experimental data

• Entrapped air bubbles are well predicted by the IBM but are not resolved in the OpenFOAM

Exp: t ≈ 0.24s

Exp: t ≈ 0.26s

Dropping height: 300mm

Summary

I. There are still many challenges in marine engineering which affect safe operation and adequate design.

II. We have tried to develop next generation tools/methods for modelling waves and wave-structure interaction to tackle the challenges.

III. The results obtained so far by using fully nonlinear potential methods, full nonlinear viscous methods and hybrid methods show that

– Possible to simulate large waves in large scale

– Possible to simulate interaction between steep/breaking waves and structures

– On the way to desirably tackle the existing challenges but a long way to go

Thank You

Acknowledgement • Supported by

EPSRC projects

(EP/L01467X/1,

EP/N008863/1 and

EP/M022382/1)

• Some results are

produced by Prof.

Sriram V (IIT

Madras, India), Dr.

Jinghua Wang, Dr.

Juntao Zhou, Dr.

Liang Yang in the

same team