Numerical Study of Strong Free surface Flow and Wave Breaking

Yi Liu

Department of Civil Engineering Johns Hopkins University

Numerical Method

air

water

interface

,a a

,w w

Fixed Eulerian grid

Coupled air-water system

Interface is represented implicitly Fixed Cartesian grid Automatically handle surface overturning, merging, and pinching

off

Variable density and viscosity NS equation

0

0

0

 

 

Level set equation

 

and

Coupled Level Set/VOF (CLSVOF) Method

0 ut

Cartesian grid

interface

water

air ,a a

,w w

Breaking of 3rd order Stokes wave (ak=0.55)

Pure LS method CLSVOF method

0 FutF

Level Set Method Volume-of-Fluid Method

Mass is not exactly conserved

Calculation of surface normal and curvature is

precise and relatively easy

Accurate calculation of surface normal and

curvature is challenging

Mass is accurately conserved

0F

0 1F

1F

VOF update

, n nF

1 1, n nF

LS reinitialize

0 ut

VOF reinitialize

n nF

1n

Construct interface using PLIC

1nF

,n n

*

**

Volume Flux calc

1nF

,nF f

0

0

0

(Sussman & Puckett 1998)

[.]

Interface Jump Conditions

Stress discontinuity

00

2

1

TNIp

TTN

Numerical simulation of a static air bubble without gravity effect

Density and viscosity discontinuity[ ][ ]

w a

w a

bubble

uNumerical simulation of multi-layer Couette flow

Continuous Surface Force Method

Ghost Fluid Method

[.]

11

10.1

High Performance Computing (HPC) on Supercomputers Large-scale parallel computing is necessary for CPU- and memory-intensive

simulations of wave-turbulence-body interactions. Message Passing Interface (MPI) is used for parallelization. Our parallel codes show excellent performance on supercomputers.

Cray XE620,224 cores, 192.4T Flops

SGI Altix ICE15,360 cores, 172T Flops

Cray XT48,584 cores, 72.3T Flops

Cray XE611648 cores, 107.2T Flops

# of cores MPI+MPI_SYNC I/O Imbalance%

16 1.7% 1.1% 0.5

32 4.5% 1.0% 0.8

64 9.4% 1.3% 1.8

128 8.6% 2.3% 1.5

256 15.2% 4.1% 2.4

Profiling result of the CLSVOF code

Computing resources provided by DoD High Performance Computing Modernization Program (HPCMP).

Research Topics

1. Numerical study of breaking waves with different intensity.

2. Numerical study of the interaction between wind turbulence and wave breaking.

3. Numerical study of the wind wave generation and growth.

4. Mechanistic study of strong free surface turbulence.

5. Hybrid Euler-Lagrangian method for the numerical simulation of wave breaking.

6. Multi-scale simulation of wind-wave-structure interaction.

(ak)0=0.3 (ak)0=0.35 (ak)0=0.4 (ak)0=0.44 (ak)0=0.55

Topic 1: Breaking Waves without Wind Effect To investigate the breaking criteria and the energy dissipation

Energy Evolution during Wave Breaking

(ak)0=0.55

(ak)0=0.44

(ak)0=0.40

(ak)0=0.35

(ak)0=0.3

For all the breaking cases, there are three regimes of energy evolution: (a) initial slow decay; (b) strong decay; and (c) slow decay afterward.

The duration of initial slow decay decreases as the wave steepness increases. The strong decay lasts for approximately 2 wave periods. The total energy loss increases with wave steepness. For steep waves, the relative loss of wave energy is independent of the wave

steepness.

2 2

2total k pu vE E E dxdy gydxdy

Topic 2: Wind Turbulence over Breaking Waves

Problem Setup

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

To investigate the interaction between wind turbulence and the breaking wave

Velocity field at both air and water side

Wind stress and drag coefficient Air flow separation Turbulence and current

generation by breaking Energy dissipation rate

Simulation Results

Wave Breaking under Different Wind Speeds

U10=5.06m/s U10=11.08m/s

U10=14.97m/s U10=19.70m/s

Breaking associated with high wind appears more violent.

The breaking affects the turbulence in the wind.

Splash-up enhances turbulent mixing in the airflow.

spume

jet

Plunging Breaking and Vortex Generation

T=1.33T

T=1.78T

T=2.67T

T=2.22T

Plunging breaker generate large mean vortex structure.

Small co-rotating vortices coalesce into larger ones.

Spilling breaker only generate mean shear.

Topic 3: Wave Evolution from Flat under Turbulent Wind

Amplitude spectrumEvolution of rms of surface elevation

To investigate the wave generation and growth under turbulent wind

Wave field evolution and growth rate Spectral characteristics and its

evolution Frequency downshifting Comparison with JONWAP spectrum

Topic 4: Mechanistic Study of Strong Free-Surface TurbulenceTo investigate the interaction between free surface and underlying

turbulence Features of free surface in different flow

regimes. Thickness of intermittency layer and the

distribution of intermittency factor. Scale dependence of surface structure on

Froude and Weber numbers. Effect of Froude and Weber numbers on

turbulence kinetic energy.

Instantaneous Surface Features

Small surface elevation

Gravity dominated

Surface tension dominated

Very strong turbulence

Breaking surface

Marginal breaking

Dimples and scars are observed on free surface.

Dimples are generated due to low pressure at the core of surface-connected vortices.

Scars are associated with near-surface horizontal vortices.

Knobs are observed on free surface.

The surface is smooth and dominated by the large-scale structures.

Breaking waves and complex structures are observed on free surface.

2 2Fr U gL 2We U L

Splat and Anti-Splat

Strong vertical motion towards the surface; Radial horizontal flow motion; Induces strong pressure at the surface; Accompanied by horizontal vortex pair; Generates vortex in the air.

Splat:

Anti-splat: Formed when radial motion encounters; Downward flow motion; Has long and thin shape.

Vortex pair

Splat

Vortex in the water

Splat-induced vortex in air

Splat

Anti-splat

Level SetSPH

Topic 5: Level Set-SPH Coupled Simulation for Wave BreakingTo improve the resolution locally and capture fine scale droplets formed

by breaking

Smoothed Particle Hydrodynamics (SPH) Method

( ) ( ') ( ' ) 'f x f x x x dx SPH interpolation:

1 1

( ) ( , )N N

j ji j i j j ij

j jj j

m mf x f W x x h f W

1),(

xdhxxW )'(),(lim0

xxhxxWh

where kernel function w satisfies

Continuity equation:

1 1

N Ni

j i j ij j ij ijj j

dm v v W m v W

dt

Momentum conservation equations:

2 2 2 2j ij j j iji i i i

j jj ji j i i j i

p W Wdv pm m

dt x x

strain rate 1 1 1

23

N N Nj ij j ij j

i ji ji ji i ijj j jj i j i j

m W m W mv v v W

x x

0

1p B

Equation of state (EOS):

Weakly compressible for ca>10cp

ca

cp

Acoustic wave speedSurface wave speed

Breaking Wave Simulation with SPH(ak)0=0.55, 3rd-order Stokes wave

Dispersed water parcels are generated in the breaking region.

Particle located far from the breaking wave crest has an orbital motion.

Particle located at the breaking crest starts with a circular motion. After it reaches the wave crest, it moves forward with the breaking jet, falls down to the water, and then bounces up with the splash. Particle trajectory

Breaking onset Jet touchdown

apBCInflow BC

objectv

air

wave

water

HOS simulation of wave fields

coupled LS/VOF/GFM for air-water simulation

LES of wind turbulence

IBM for structure

Topic 6: Multi-scale Simulation of Wind-Wave-Structure InteractionTo investigate the wave effect on the wind forcing over structures

Immersed Boundary Method for Flow-Structure Interaction

nn b

bu u

f RHSt

0

bu RHS f

intu

In immersed boundary method, the structure is represented byadding a force term into the momentum equation. Then the governing equations become

Direct discrete forcing approach is used to calculate the boundary force

forcing points

fluid

solid

x

x

boundary points

f b

Immersed Structure

f

b

Fluid

,

u

where

2

1 1 2( ) ( ) Re

1( )

RHS p D

kFr We

is interpolated on the forcing point from its nearby flow points and the corresponding boundary point. bu

An immersed boundary method is used to simulate the flow-structure interaction.

fluid points

weaker horseshoe vortexstronger horseshoe vortex

Dependence of Wind Load on Wave Phase

The wave phase dependence of wind load may be induced by:

Phase dependence inherits from inflow field Variation of horseshoe vortex in front of the object

wave crest reaches the frontal face wave trough reaches the frontal face

Angle Effect to Force and Moment Coefficients

0 30 60

For 0°attack angle case, the strongest flow separation happens on the two side walls and the lowest pressure happens on those two side walls. The pressure in the wake is a little bit higher than the other two cases.

For 30°attack angle case, the strongest flow separation happens on the back and one side walls.

For 60°attack angle case, one side wall faces the inflow and the pressure on the original front is not so high. The wake region is larger than the other two cases.