from eigenfunction expansions to cfd in 25 years. is it enough … · 2019. 2. 8. · ih-foam...
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From Eigenfunction Expansions to CFD
in 25 years.Is it enough progress?
Iñigo J. Losada
Environmental Hydraulics Institute “IHCantabria”Universidad de Cantabria, Santander-SPAIN
Water Wave Mechanics and Coastal Engineering
Real Academia de Ingeniería
Wave transformation
Coastal structures
Developing water wave models for coastal engineering
Seaward slope geometry Vertical breakwater
High-mound breakwater
Rubble-mound breakwater
Crest
Submerged breakwater
Overwashed breakwater
Non-overtopped structure
Permeability Impervious structure
Porous breakwater
EnergyReflective sctructures
Transmitted wave energy
Dissipative structure
Composite structures
NMM
Wave transformation:
Refraction, diffraction and shoaling
(Intermediate and shallow water)
Deep water
Wave overtopping
Loads at the caisson
Incident wavesLoads at the
armour layer
Transmitted waves
Reflected wave
Seaward Leeward
Run-up / Run-down
Reflection
Transmission
Dissipation
(Ko
rten
ha
us
& O
um
era
ci, 1
99
8)
SWL
hb
hs
SWL
hb
hs
SWL
hbhs
SWL
hb
hs
h*<0.3 0.3<h*<0.6 0.9<h*<1.0 h*>1.00.6<h*<0.9
Vertical Breakwater
Low mound
Breakwater
High Mound
Composite Breakwater
Crown Walls
Rubble Mound Breakwater
Small waves Large waves
H*s<0.35 H*s>0.35
Small waves Large waves
0.1<H*s<0.2 0.2<H*s<0.6
Large waves Very large waves
0.2<H*s<0.6 H*s>0.6
Small waves
0.1<H*s<0.2
Moderate Berm Wide Berm
0.12<B*<0.4 B*>0.6
Narrow Berm
0.08<B*<0.12
5
2.5
0
7.5
0 0.2 0.4 0 0.1 0.2 0 0.1 0.2 0 0.1 0.2 t/T
Fhmax Fhq
5
2.5
0
7.5
5
2.5
0
7.5
5
2.5
0
7.5
t/Tt/Tt/T
Fhmax
Fhq
Fhmax
Fhq
Quasi-standing waveSlightly breaking
wave
Impact loads Broken waves
Fhmax
Fhq
F*h F*
hF*
h
F*h
High mound
Breakwater
Wave loads
Models based on potential flow theory
MAIN APPROACHES
Models based on Navier-Stokes equations
LagrangianEulerian
SPH
(Smoothed
Particle
Hydrodynamics)
DNS (Direct numerical Simulation)
LES (Large Eddy Simulation)
RANS/VARANS
Reynolds Averaged
Boussinesq-type
EquationsNonlinear
Shallow Water
Equations
Eigenfunction
Expansions
1990-2014
Stokes
Waves
Tony’s top ten
Source: SCOPUSWave interaction with vegetation
Torremolinos-ICCE 1988
1983Prentice Hall
World Scientific 1991
10
Multiple scale perturbation method
Parabolic equation for combined-refraction-diffraction
Crank-Nicholson scheme
REF-DIF model First course 1989/90
Tony’s top ten
Source: SCOPUS
13
14
15
16
17
Problems:
• Complex wave dispersion equation
• Newton-Raphson --Mode swapping
• Orthogonality of eigenfunctions with complex wave numbers
• Solving system of equations
18
19
20
21
Kirby
Svendsen
Kobayashi
Dalrymple
24
25
New mild-slope equation
Porous flow is included
26
27
28
Surf zone models 1-D and 2-D
Extended Boussinesq equations (Nwogu, 1993)
Fully nonlinear Boussinesq equations (Wei et al. 1995)
modified eddy viscosity model
slot technique to represent the moving shoreline and dry land
29
30
Incoming solitary wave
31
Porous
Solid
Symmetric inlet/bay connected to sea
Coupled boundary value problems
Fourier transforms + eigenfunction expansions
Helmholtz equation
System resonances to short and long wave forcings
Models based on potential flow theory
MAIN APPROACHES
Models based on Navier-Stokes equations
LagrangianEulerian
SPH
(Smoothed
Particle
Hydrodynamics)
DNS (Direct numerical Simulation)
LES (Large Eddy Simulation)
RANS/VARANS
Reynolds Averaged
Boussinesq-type
EquationsNonlinear
Shallow Water
Equations
Eigenfunction
Expansions
1999-2000
Stokes
WavesDIVORCE
36
37
38
What’s IH-2VOF ? Losada et al. (2008)
• 2-D Navier-Stokes model
• Developed at IH-Cantabria
• RANS equations
• Finite differences scheme
• Porous media flow is considered: Forcheimer model
• Turbulence model: k-Epsilon
• Free surface tracking: VOF (Volume de Fluid)
Experimental set-up
+0.8
45 m44 m 46 m 47 m
0 m
1 m
1,04
0,7
0,12
0,3
2
1
2
1
0,10,1
Dimension in meters
WG
-7
WG
-8
WG
-9
WG
-10
WG
-11
WG
-12
WG
-13
45 m44 m43 m 46 m 47 m0 m
1 m
42 m41 m40 m39 m38 m37 m36 m35 m34 m33 m32 m31 m30 m29 m28 m27 m26 m25 m24 m23 m22 m21 m20 m19 m18 m17 m
WG
-1
WG
-2
WG
-3
WG
-4
WG
-5
WG
-6
WG
-1
16 m15 m14 m13 m12 m11 m10 m9 m8 m7 m6 m5 m4 m3 m2 m1 m0 m
WG
-7
WG
-8
WG
-9
WG
-10
WG
-11
WG
-12
WG
-13
45 m44 m43 m 46 m 47 m
0 m
1 m
42 m41 m40 m39 m38 m37 m36 m
WG
-2
WG
-3
WG
-4
WG
-5
WG
-6
WG
-14
WG
-14
Free surface gauges location
45 m44 m 46 m 47 m
0 m
1 m
PG-1
PG-2
PG-3
PG-4
PG-5
PG-6
PG
-7
PG
-8
PG
-9
PG
-10
Pressure gauges locationGeometry
University of Cantabria
- Wave flume -
- 68.5 m long
- 2 m wide
- 2 m high
- Mixed piston-pendulum
type wave maker
- Active Wave Absorption
System (AWACS®)
Guanche, R., I.J. Losada and J.L. Lara. (2009). Numerical
analysis of wave loads for coastal structure stability, Ocean
engineering, ELSEVIER, 56, 543-558
Horizontal forces (FH), Vertical forces (FV), Horizontal moment (MFH) and Vertical Moment
(MFV) time evolution
Stability analysis
Irregular case: Hs=0.15m Tp=5s h=0.8m
Maximum horizontal (FH) and vertical
forces (FV)
Stability analysis: Irregular
waves
Maximum horizontal (MFH) and vertical
moments (MFV)
Irregular waves
Mean error Std deviation
Max FH 2.19% ±6.82%
Max FV -0.69% ±6.80%
Max MFH -2.11% ±7.68%
Max MFHV -0.61% ±7.01%
Iregular waves
0
0.5
1
1.5
2
2.5
3
0 0.5 1 1.5 2 2.5 3
Lab(kN/m)
Nu
m(k
N/m
)
Fhmax
Smax
Irregular waves
0
0.25
0.5
0.75
1
1.25
1.5
0 0.25 0.5 0.75 1 1.25 1.5
Lab(kN/m)
Nu
m(k
N/m
)
M FHmax
M FVmax
Conventional geometry Non-conventional geometry
Motivation
0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500
-8-6-4-20 2 4 6 8 101214
Run-up analysis
t(s)
Ru
n-u
p(m
)
SWL=+2.8 m.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150
10
20
30
40
50
60
70
Histogram
Nu
mb
er
of
even
ts
Run-up(m)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150 0.10.20.30.40.50.60.70.80.91
Pro
bab
ilit
y
Run-up(m)
Probability distribution function
500 550 600 650 700 750 800 850
-40
-30
-20
-10
0
10
20
x(m)
y(m
)
500 550 600 650 700 750 800 850
-40
-30
-20
-10
0
10
20
x(m)
y(m
)
Overtopping analysis
0 500 1000 1500 2000 2500 3000 35000
200
400
600
t(s)
m3/m
Qmean
overtopping: 0.18204m3/s/m
0 500 1000 1500 2000 2500 3000 35000
50
100
t(s)
m3/m
Volmax
overtopping: 84.6662m3/m
0 500 1000 1500 2000 2500 3000 35000
5
10
15
t(s)
m
Layer thicknessmax
overtopping: 6m
0 500 1000 1500 2000 2500 3000 35000
5
10
15
20
t(s)
m/s
Velmax
overtopping: 6.9296m/s
500 550 600 650 700 750 800 850
-40
-30
-20
-10
0
10
20
Simulated Geometry
x(m)
y(m
)
Number of waves= 302H
s= 8.69 m; H
m0= 8.86 m
Hrms
= 6.12 m; Hmean
= 5.36 m
Hmax
= 15.84 m; time=1084.84s (Hmax
/Hs= 1.82 eta
max/H
max= 0.56 )
Tm
= 11.85 s
Ts= 16.11 s
Tp= 15.85 s
T(Hmax
)= 13.93 s
Results summary
Run-up Run-up
mean= 8.43 m
Run-up2%
= 12.18 m
Run-upmax
= 12.18 m
Overtopping
Mean overtopping discharge: 0.18204 m3/m/s
Maximum overtopping event: 84.66 m3/m
Maximum overtopping velocity: 6.92m/s
Maximum layer thickness: 6.0 m
Conventional
4.3b0.2,a
;··exp·81.9 3
s
c
sH
Rba
H
q
Franco et al. (1994) Eurotop (2008)
Plain vertical walls (d*>0.3)
300
0.04·exp 2.6· ;9.81·
c
mm
Rq
HH
Mean Overtopping discharge
Case IH2VOF Eurotop(2008) Franco et al. (1994)
Conventional 0.1820 m3/m/s 0.1917 m3m/s 0.1321 m3m/s
Non
Conventional0.1601 m3/m/s 0.1531 m3m/s 0.0894 m3m/s
48
CERC Meeting ICCE 2012-Baltimore
PROS:
• Free and open source.
• Widely used in industry.
• 3D RANS equations.
• Finite volume discretization.
• Two-phase incompressible flow.
CONS:
• No native wave generation and absorption.
• No handling of two-phase porous media flows.
Why OpenFOAM?
New solver developed on OpenFOAM
IH-FOAM solves Reynolds-averaged Navier-Stokes equations fortwo phases through finite volumes in three dimensions. It includesa large number of turbulence models like k-ε, k-ω SST or LES.
Porous media are solved by VARANS equations (Volume-Averaged/Reynolds-Averaged Navier-Stokes).
Free surface is trackedthanks to a VOF technique
Higuera, P., Lara, J.L., Losada, I.J. (2014) “Three-dimensional interaction of waves and porous coastal structures using OpenFOAM. Part I: Formulation and validation”, Coastal Engineering, Vol 83, pp 243-258
Higuera, P., Lara, J.L., Losada, I.J. (2013) “Realistic wave generation and active wave absorption for Navier-Stokes models. Application to OpenFOAM”, Coastal Engineering, Vol 71, pp 102-118
Higuera, P., Lara, J.L., Losada, I.J. (2014) “Simulating coastal engineering processeswithOpenFOAM. Coastal Engineering, Vol 71, pp 119-134
Higuera, P., Lara, J.L., Losada, I.J. (2014) “Three-dimensional interaction of waves and porous coastal structures using OpenFOAM. Part II: Application”, Coastal Engineering, Vol 83, pp 259-270
52
ICCE 2014-Seoul
IHFoam-Large scale application
• Design sea state (475 years return period)
– Hs = 6 m, Tp = 18 s, Dir: N15ºE, Tide: + 5,5 m
• Domain
– 500 x 700 x 34 m
– 10 million cells
• Simulation time
– 25 s/day@ 128 processors
N
Smallest cell 0,25 m x 0,375 m x 0,125 m
Propagation and impact of the selected wave group
DYNAMIC PRESSURE
FORCES
Here is where we are after 25 years!
Vielen Dank for these 25 years!
and
Enhorabuena por tu ingreso en la Academia
Water Wave Mechanics and Coastal
Engineering
Real Academia de Ingeniería