numerical study of wave and submerged breakwater interaction (data-driven and physical-based model...

Numerical study of wave and Numerical study of wave and submerged breakwater interactionsubmerged breakwater interaction

(Data-driven and Physical-based Model for characterization of Hydrology, Hydraulics,

Oceanography and Climate Change) IMS-NUS

PHUNG Dang Hieu

Vietnam Institute of Meteorology, Hydrology and Environment

Email: [email protected]

Waves on coasts are beautiful

They are violent too!

Fig.1: Overtopping of seawall onto main railway - Saltcoats,Scotland

(photo: Alan Brampton)

Fig. 2: Heugh Breakwater, Hartlepool, UK(photo: George Motyka, HR Wallingford)

To reduce wave energy

Breakwater – Submerged– Seawall

LandLandbreakingbreaking

Seawall supported by porous partsSeawall supported by porous parts

Example of Seawall atMabori, Yokosuka, Japan

Structure design diagram

Design Wave Conditions

Physical Experiments

Numerical Simulations

Wave pressures & Forces

upon structures

Wave Reflection, Transmission

Wave Run-up, Rundown,

Overtopping

Velocity field, Turbulence

Information For Breakwater & Seawall designs

Some problems of Experiments related to Waves

1. Physical experiment of Small scale: – Scale effects– Undesired Re-reflected waves

2. Lager Scale experiment - Costly3. Numerical Experiment

– Cheap– Avoid scale effects and Re-reflected wavesDifficulties: Integrated problems related to the advanced

knowledge on Fluid Dynamics, Numerical Methods and Programming Techniques.

What do we want to do?

• Develop a Numerical Wave Channel– Navier-Stokes Eq.– Simulation of wave breaking– Simulation of wave and structure

interaction• Do Numerical experiments:

– Deformation of water surface– Transformation of water waves; wave-

porous structure interaction

Concept of numerical wave channel

water

air Free surface boundary

Non-reflective wave maker boundary Open boundary

Porous structure

Solid boundary

Wave absorber

Governing Equations

• Continuity Eq.

• 2D Modified Navier-Stokes Eqs. (Sakakiyama & Kajima, 1992) extended to porous media

vzx qz

w

x

u

xxxezexv

v MRuDx

w

z

u

zx

u

xx

p

dt

du

2

zzzvezexv

v MRwDgz

w

zz

u

x

w

xz

p

dt

dw

2

(1)

(2)

(3)

• where:

2212

1wuu

x

CR x

Dx

2212

1wuw

z

CR z

Dz

dt

duCM vMx )1(

dt

dwCM vMz )1(

CD : the drag coefficient

CM: the inertia coefficient

: the porosity

x ,z: areal porosities in the x and z projections

e: kinematic eddy viscosity =+t

(4)

(5)

Turbulence model

• Smangorinski’s turbulent eddy viscosity for the contribution of sub-grid scale:

2/1,,

2 ).2( zxzxst SSC

x

w

z

uS zx 2

1,

2/1)( zx

(6)

Free-surface modeling

• Method of VOF (Volume of fluid) (Hirt & Nichols, 1981) is used:

Fzxv q

z

Fw

x

Fu

t

F

F =Volume of water

Cell Volume; 10 F

(4)

qF : the source of F due to wave generation source method

F = 1 means the cell is full of waterF = 0 means the cell is air cell0< F <1 means the cell contains the free surface

Free surface approximation

Nature free surface

PCIC - VOF approximation

PLIC-VOF approximation

water

air

1

.5 0

11

1 1

1

1

1

1

11

1 1

11

1

11

1

1

1

1

111

1

1

1

1

1

1

1

1

1

1

1

1

1

.4

.6

0

.4.6

.1

.7

.1

.2

.9

.6 .5 .6 .4

.4

.7 .2

.9

0

0

Simple Line Interface Construction- SLIC approximation

Piecewise Linear Interface Construction- PLIC approximation

Natural free surface

Hirt&Nichols(1981)

present study

Interface reconstruction

nij

ni-1/2 j+1/2 ni+1/2 j+1/2

ni-1/2 j-1/2

ni+1/2 j-1/2

xi

yj

P1

P2

yxFijPOPS 21

S POP 21

O

Numerical flux approximation

u>0

u t

ut

u<0

Donor cell

Acceptor cell

Local free surface

Acceptor cell

Donor cell

u>0

u t

ut

u<0

Donor cell

Acceptor cell

Local free surface

Acceptor cell

Donor cell

SLIC-VOF approximation (Hirt&Nichols, 1981)

PLIC-VOF approximation (Present study)

Non-reflective wave maker (none reflective wave boundary)

0 1 2 3 4 5 6 7 8distance (m)

30

35

40

45

50

55

waterlevel(cm)

Damping zoneFree surface elevation

Wave generating

source

Vertical wall

Progressive wave area Standing wave area

Tt

d

d

x

U

Ttd

d

x

U

T

t

q

s

i

s

i

s

i

s

i

s

3 2

3 if 2

3

MODEL TEST

• Deformation of water surface due to Gravity– TEST1: Dam-break problem (Martin &

Moyce’s Expt., 1952)– TEST2: Unsteady Flow – TEST3: Flow separation– TEST4: Flying water (Koshizuka et al., 1995)

• Standing waves– Non-reflective boundary– Wave overtopping of a vertical wall

TEST1: Dam-break

0 5 10 15 20horizontal direction (cm)

0

5

10

15Verticaldirection(cm)

1m/s


0

5

10

15

Verticaldirection(cm)

1m/s


0

5

10

15


1m/s


0

5

10

15


1m/s

time=0s time=0.085s

time=0.125s time=0.21s

L

2L

(Martin & Moyce , 1952)

Time history of leading edge of the water

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5 4

x/L

Cal. (Hirt&Nichols [4], DELTY=0.025)

Cal. (Hirt&Nichols [4], DELTY=0.05)

Expt. (Martin & Moyce [27], 2.25in)

Cal. (present model)

Lgt /2

0 2 4 6 8 10 12 14 16 18 20 22

horizontal direction (cm)

0

5

10

15


1m/s

x

L

X

Z

10 20 30 40 50

10

20

30

40

502m/s

solid wall

TEST - 2

Frame 001 13 Jan 2008 GRAPH TEST2

Initial water column

TEST3

X

Z

10 20 30 40 50

10

20

30

40

502m/s

solid wall

TEST - 3

Frame 001 13 Jan 2008 GRAPH


TEST4

X

Z

10 20 30 40 50

10

20

30

40

502m/s

TEST - 4

Frame 001 13 Jan 2008 GRAPH


Solid obstacle

(Koshizuka et al’s Experiment (1995)

TEST4

0 0.1 0.2 0.3 0.4 0.5X (m)

0

10

20

30

40

50

Z(cm)

1.0000.9380.8750.8130.7500.6880.6250.5630.5000.4380.3750.3130.2500.1880.1250.0500.000

F %

HYDRAULICS LABBORATORY,SAITAMA UNIVERSITY

DAMBREAKING PROBLEM

0 0.1 0.2 0.3 0.4 0.5X (m)

0

10

20

30

40

50

Z(cm)

1.0000.9380.8750.8130.7500.6880.6250.5630.5000.4380.3750.3130.2500.1880.1250.0500.000

F %

HYDRAULICS LABBORATORY,SAITAMA UNIVERSITY

DAMBREAKING PROBLEM

(Koshizuka et al., 1995) Simulated Results

time=0.04s

time=0.05s

obstacle

MODEL TEST WITH WAVES

• Standing waves• Wave overtopping• Wave breaking

Regular waves in front of a vertical wall

0

5

10

15

20

25

-3 -2.5 -2 -1.5 -1 -0.5 0

x(m)

H(c

m)

Numerical

Stokes 3rd theory (Kr=1.00)

Stokes 3rd theory (Kr=0.96)

Vertical wall

wave overtopping of a vertical wall

G2 G1G12

11 x 17cm =187cm

17cm

h= 42.5cm water

air

Wave conditions: Hi= 8.8 & 10.3cm T = 1.6s

SWL

Wave overtopping

hc=8cm

Experimental conditions

Time profile of water surface at the wave gauge G1

-0.1

-0.05

0

0.05

0.1

0.15

8 10 12 14 16 18 20 22 24 26 28 30

time (s)

Wat

er s

urf

ace

elev

atio

n (

m)

NumericalExperimental

Effects of re-reflected waves

Time profile of water surface at the wave gauge G5

-0.1

-0.05

0

0.05

0.1

0.15

8 10 12 14 16 18 20 22 24 26 28 30

time (s)

Wat

er s

urf

ace

elev

atio

n (

m)

NumericalExperimental


Wave height distribution

0

0.5

1

1.5

2

2.5

3

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0

x / L

H/H

I

Simulated

Measured

Vertical wall

L: the incident wave length

Overtopping water

0

50

100

150

8 10 12 14 16 18 20 22 24 26 28 30

time (s)

Tot

al d

isch

arge

(cm

3/cm

)

0

50

100

150

Ove

rtop

ping

rat

e (

cm3/

cm/s

)

Measured total dischargeSimulated total dischargeSimulated overtopping rate

Wave condition: Hi=8.8cm, T=1.6s


Wave breaking

6 8 10 12 14Cross shore distance (m)

0.2

0.3

0.4

0.5

0.6

Ver

tical

dis

tan

ce(m

)

Breaking point (x=6.4m from the original point)

Sloping bottom s=1/35

SWL

Run-up Area

Experimental conditions by Ting & Kirby (1994)

Surf zone

(Hi=12.5cm, T=2s)

x=7.275m

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-2 0 2 4 6 8 10 12

x (m)

Surf

ace

ele

vati

on (

m)

present cal. resultsExpt. Data (Ting & Kirby, 1994)

Cal. results (Bradford, 2000)Cal. results (Zhao et al.,2000)

Comparison of wave height distribution

Breaking point

Wave crest curves

Wave trough curves

2004)

Velocity comparisons at x=7.275m

-0.6-0.4-0.2

00.20.40.6

0 0.5 1

t/T

u (m

/s)

-0.6-0.4-0.2

00.20.40.6

0 0.5 1

t/T

u (m

/s)

-0.4

-0.2

0

0.2

0.4

0 0.5 1

t/Tw

(m

/s)

-0.4

-0.2

0

0.2

0.4

0 0.5 1

t/T

w (

m/s

)

At z =-4cm

At z =-8cm

Horizontal velocity

Vertical velocity

Interaction of Wave and Porous submerged break water

h=37.6cm33cm

115cm

29cm

38 capacitance wave gauges

H=9.2cmT=1.6s

SWL

Wave absorber

air

water

Porous break water

x=0x

G1 G12 G17 G31 G34 G38

1. What is the influence of inertia and drag coefficients on

wave height distributions ?2. What is the influence of the porosity of the

breakwater on the wave reflection and transmission?

3. What is the effective height of the submerged breakwater?

Objective: to answer the above questions partly by numerical simulations

Influence of inertia coefficient on the wave height distribution

4

6

8

10

12

14

-200 -100 0 100 200

Horizontal distance (cm)

H(c

m)

Exp. DataCm=0.2Cm=0.6Cm=1.0Cm=1.5

Breaking point

Cd=3.5

1.0<Cm<1.5

Influence of drag coefficient on the wave height distribution

4

6

8

10

12

14

-200 -100 0 100 200

horizontal distance (cm)

H (

cm)

Exp. DataCd=0.5Cd=1.0Cd=1.5Cd=2.5Cd=3.0Cd=3.5Cd=4.0

Cm=1.2

Breaking point

The best combination: Cd=1.5, Cm=1.2

water surface elevations at the off-shore side of the breakwater

-0.1

-0.05

0

0.05

0.1

14 14.5 15 15.5 16 16.5 17 17.5 18

time (s)

(m

)

MeasuredSimulated

(G1)

-0.1

-0.05

0

0.05

0.1

14 14.5 15 15.5 16 16.5 17 17.5 18

time (s)

(m

)

MeasuredSimulated

(G17)

Water surface elevations at the rear side of the breakwater

-0.1

-0.05

0

0.05

0.1

14 14.5 15 15.5 16 16.5 17 17.5 18

time (s)

(m

)

MeasuredSimulated

(G31)

-0.1

-0.05

0

0.05

0.1

14 14.5 15 15.5 16 16.5 17 17.5 18

time (s)

(m

)

MeasuredSimulated(G38)

Variation of Reflection, Transmission and Dissipation Coefficients versus different Porosities

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

Porosity

KR, K

T, K

D

K T K D

K R

Porosity of Structure

Optimal Depth

h

b

d

Consideration: - top width of the breakwater is fixed, - slope of the breakwater is fixed - change the depth on the top of the breakwaterFind: Variation of Reflection, Transmission Coefficients

Results

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3 3.5 4

d/H I

KR, K

T, K

D

REMARKS

1. There are many practical problems related with computational fluid dynamics need to be simulated in which wave-structure interaction, shore erosion, tsunami force and run-up, casting process are few examples.

2. A Numerical Wave Channel could be very useful for initial experiments of practical problems before any serious consideration in a costly physical experiment later on (water wave-related problem only).

3. Investigations on effects of wind on wave overtopping processes could be a challenging topic for the present research.

THANK YOU

Calculation of Wave Energy and Coefficients

numerical study of wave and submerged breakwater interaction (data-driven and physical-based model...

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