Numerical study of wave and submerged 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

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 Land breaking Seawall supported by porous parts

Example of Seawall at Mabori, 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 - Costly 3.Numerical Experiment –Cheap –Avoid scale effects and Re-reflected waves Difficulties : 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 boundaryOpen boundary Porous structure Solid boundary Wave absorber

Governing Equations Continuity Eq. 2D Modified Navier-Stokes Eqs. (Sakakiyama & Kajima, 1992) extended to porous media (1) (2) (3)

where: C D : the drag coefficient C M : 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: (6)

Free-surface modeling Method of VOF (Volume of fluid) (Hirt & Nichols, 1981) is used: F = Volume of water Cell Volume ; (4) q F : the source of F due to wave generation source method F = 1 means the cell is full of water F = 0 means the cell is air cell 0< F <1 means the cell contains the free surface

Free surface approximation water air Simple Line Interface Construction- SLIC approximation Piecewise Linear Interface Construction- PLIC approximation Natural free surface Hirt&Nichols (1981) present study

Interface reconstruction P1 P2 O

Numerical flux approximation SLIC-VOF approximation (Hirt&Nichols, 1981) PLIC-VOF approximation (Present study)

Non-reflective wave maker (none reflective wave boundary) Damping zone Free surface elevation Wave generating source Vertical wall Progressive wave areaStanding wave area

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 time=0s time=0.085s time=0.125s time=0.21s L 2L2L (Martin & Moyce, 1952)

Time history of leading edge of the water

TEST2 Initial water column

TEST3 Initial water column

TEST4 Initial water column Solid obstacle (Koshizuka et al’s Experiment (1995)

TEST4 (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 Vertical wall

wave overtopping of a vertical wall G2G1 G12 11 x 17cm =187cm 17cm h= 42.5cm water air Wave conditions: H i = 8.8 & 10.3cm T = 1.6s SWL Wave overtopping h c =8cm Experimental conditions

Time profile of water surface at the wave gauge G1 Effects of re-reflected waves

Time profile of water surface at the wave gauge G5 Effects of re-reflected waves

Wave height distribution Vertical wall L: the incident wave length

Overtopping water Wave condition: Hi=8.8cm, T=1.6s Effects of re-reflected waves

Wave breaking 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

Comparison of wave height distribution Breaking point Wave crest curves Wave trough curves 2004)

Velocity comparisons at x=7.275m At z =-4cm At z =-8cm Horizontal velocityVertical velocity

Interaction of Wave and Porous submerged break water h=37.6cm 33cm 115cm 29cm 38 capacitance wave gauges H=9.2cm T=1.6s SWL Wave absorber air water Porous break water x=0 x G1G12G17 G31G34G38 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 Breaking point Cd= <Cm<1.5

Influence of drag coefficient on the wave height distribution 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

Water surface elevations at the rear side of the breakwater

Variation of Reflection, Transmission and Dissipation Coefficients versus different Porosities Porosity of Structure

Optimal Depth d Consideration: - top width of the breakwater is fixed, - slope of the breakwater is fixed - change the depth on the top of the breakwater Find: Variation of Reflection, Transmission Coefficients

Results

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