numerical study of wave and submerged breakwater interaction (data-driven and physical-based model...
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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 20horizontal direction (cm)
0
5
10
15
Verticaldirection(cm)
1m/s
0 5 10 15 20horizontal direction (cm)
0
5
10
15
Verticaldirection(cm)
1m/s
0 5 10 15 20horizontal direction (cm)
0
5
10
15
Verticaldirection(cm)
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
Verticaldirection(cm)
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
Initial water column
TEST4
X
Z
10 20 30 40 50
10
20
30
40
502m/s
TEST - 4
Frame 001 13 Jan 2008 GRAPH
Initial water column
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
Effects of re-reflected waves
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
Effects of re-reflected waves
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