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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.