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OpenFOAM in Wave and Offshore CFD
Capabilities of the Naval Hydro Pack
Hrvoje Jasak
Wikki Ltd. United Kingdom
Faculty of Mechanical Engineering and Naval Architecture, Uni Zagreb, Croatia
University of Castellon, 27 September 2017
OpenFOAM in Wave and Offshore CFD – p. 1
Outline
Objective
• Demonstrate technical capabilities of the Naval Hydro Pack in wave modelling (and
global performance) of off-shore structures
• Describe recent improvements in free surface numerics and wave generation
• Provide a review of relevant validation and verification data
Topics
• Numerics improvement topics
◦ Ghost fluid method for accurate interface resolution
◦ Geometric VOF method: isoAdvector
• Summary of Validation & Verification (V&V) of the Naval Hydro pack for
◦ Wave propagation including regular and irregular sea states
◦ Higher order forces evaluation for static structures
◦ Detailed green sea V&V: comparing numerical uncertainties with
experimental uncertainties
• Summary
OpenFOAM in Wave and Offshore CFD – p. 2
Ghost Fluid Method
N
dry cell, ψN <0
P
wet cell, ψP >0
ψ=0β−
β+
df
xΓ
OpenFOAM in Wave and Offshore CFD – p. 3
Ghost Fluid Method
Interface Jump Conditions in Free Surface Flows
• In free surface flows, a discrete surface discontinuity exists with a sharp change in
properties: ρ, ν: proper handling is needed for accurate free surface simulations
• Huang et.al. (2007) describe a ghost fluid single-phase formulation of interface
jump conditions in CFD-Ship Iowa
• Extended, modified and numerically improved treatment by Vukcevic and Jasak
(2015) with 2-phase handling is implemented in the Naval Hydro pack
◦ Perfectly clean interface: no surface jets
◦ Pressure force evaluated exactly even for a smeared VOF interface
◦ Dramatically increased efficiency and accuracy of wave modelling
α=0.5
dry cells, α<0.5
wet cells, α>0.5
N
dry cell, ψN <0
P
wet cell, ψP >0
ψ=0β−
β+
df
xΓ
OpenFOAM in Wave and Offshore CFD – p. 4
Ghost Fluid Method
Interface Jump Conditions: Derivation
• Conditionally averaged momentum equation:
∂(ρu)
∂t+∇•(ρuu) = ∇•σeff −∇pd − (g•x∇ρ)
• ρ and pd have a jump across the free surface → Taking derivatives of
discontinuous fields
• Looking at the rhs of the equation, the gradient of dynamic pressure (∇pd) is
balanced by the density gradient (∇ρ)
• The ρ-pd coupling is resolved within the momentum equation:
◦ Their imbalance will cause unphysical acceleration of the lighter phase
◦ Note: could be remedied by using fully coupled solution algorithm
OpenFOAM in Wave and Offshore CFD – p. 5
Ghost Fluid Method
Ordinary Interpolation is Insufficiently Accurate: Incorrect Gradients
x
φ
P NfΓf
φP
φN
φf
• P : cell centre,
• N : cell centre,
• f : face centre,
• Γf : interface.
OpenFOAM in Wave and Offshore CFD – p. 6
Ghost Fluid Method
Interface Jump Conditions: Derivation
• "Mixture formulation" of the momentum equation:
∂u
∂t+∇•(uu)−∇• (νe∇u) = −
1
ρ∇pd
• Dynamic pressure jump conditions at the interface:
[pd] = −[ρ]g•x
[
1
ρ∇pd
]
= 0
• Interface jumps implemented directly in discretisation operators
• Interface jump condition can be used both with level set and VOF
• . . . and smearing of the surface in VOF no longer affects the pressure forces!
• Extension to viscous force jump can be performed but currently not used
OpenFOAM in Wave and Offshore CFD – p. 7
Ghost Fluid Method
Derivation for the Two–Phase Incompressible Flow Equations
• If one takes into account the following jump conditions at the free surface
p+d
− p−d
= −(ρ+ − ρ−)g•x
1
ρ+∇p+
d−
1
ρ−∇p−
d= 0
• With the following governing equations
∇•u = 0
∂u
∂t+∇•(uu)−∇• (νe∇u) = −
1
ρ∇pd
• Pressure–density coupling moved from the momentum equation to the
pressure equation
OpenFOAM in Wave and Offshore CFD – p. 8
Ghost Fluid Method
Interpolation uses extrapolated ("ghost") values, yielding correct gradients
N
dry cell, ψN <0
P
wet cell, ψP >0
ψ=0β−
β+
df
xΓ
• Cell P and N sharean interface face,
• xΓ is the location of
the interface for thispair of dry/wet cells
OpenFOAM in Wave and Offshore CFD – p. 9
Ghost Fluid Method
The Ghost Fluid Method with Compact Stencil Support
x
φ
P NfΓf
φP
φ +
φ −φN
φ +f
φ +N
φ −fφ −P
• φ+
N: extrapolated
value at cell centre N ,
• φ−
P: extrapolated
value at cell centre P ,
• φ+,−f
: face values via
GFM interpolation.
OpenFOAM in Wave and Offshore CFD – p. 10
Interface Jump Conditions
Interface Jump Conditions: Results
• Example: 2D ramp with free surface
• Relative error for water height at the outlet is −0.34% compared to analytical
solution
• Note sharp pd jump and α distribution
• The simulation with interFoam is not stable due to spurious air velocities
OpenFOAM in Wave and Offshore CFD – p. 11
Geometric Free Surface Advection
OpenFOAM in Wave and Offshore CFD – p. 12
Geometric Free Surface Advection
isoAdvector: Accurate Free Surface Convectionvia Geometric Reconstruction
• VOF and related techniques deliver phase
conservation in free surface flows
• . . . but are poor in shape-preserving and
sensitive to mesh quality and resolution
• Johan Ronby implements a novel scalable
and parallelisable geometric reconstruc-
tion technique based on exact face flux and
iso-surface reconstruction
OpenFOAM in Wave and Offshore CFD – p. 13
Geometric Free Surface Advection
Geometric Reconstruction with the isoAdvector Scheme
• isoAdvector creates the intersection iso-surface, adjusted for the volume
fraction data in cell. VOF and velocity use point interpolation
• Intersection is tracked point-to-point within a time-step to evaluate exact face flux
• No interface smearing; minimal mesh resolution requirement; independent of
mesh structure, refinement regions; good parallelisation properties
OpenFOAM in Wave and Offshore CFD – p. 14
Regular Wave Propagation V&V
21 22 23 24 25 26 27 28 29 30t, s
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
η, m
CFDstream function
OpenFOAM in Wave and Offshore CFD – p. 15
Wave Propagation Tests
Benchmark Case: Regular Waves
• Domain for wave propagation: 60m x 6.3m
• Stream function wave:H = 0.1m, T = 3s, d = 6m
• Mild steepness, ka ≈ 0.0225
• Approximately 4 wave lengths in the domain
• 10 wave periods were simulated
• Coarse, heavily graded mesh towards the area of interest
• 11 700 cells, maximum aspect ratio is ≈ 213:1
• High aspect ratio is not an issue
OpenFOAM in Wave and Offshore CFD – p. 16
Computational Mesh
Zoomed View in the Middle Region: Wave Action
• High aspect ratio cells
• Approx 100 cells per wave length
• Approx 15 cells per wave height
OpenFOAM in Wave and Offshore CFD – p. 17
Weight (Blending) Field
Weight Field: Far Field Relaxation Zones
• Exponential function (w = 1 at the boundary and in the patch cells)
• Top figure: w = 0 (100% of the CFD solution)
• Middle figure: 0 < w < 0.5 (at least 50% CFD solution)
• Bottom figure: 0 < w < 1 (whole domain)
OpenFOAM in Wave and Offshore CFD – p. 18
Validation and Verification
Validation
• Comparison of wave elevation with the fully non–linear potential flow stream
function wave theory
Verification by performing sensitivity studies, including
• Temporal resolution study
• Mesh refinement study
• Wave reflection study
• Steepness study
• Long simulation stability assessment
• Long domain simulation
Providing Guidelines for
• Adequate time–step size
• Sufficient number of cells per wave height
• Adequate length of relaxation zones
• Possibility of global performance simulations in 3–hour storms
OpenFOAM in Wave and Offshore CFD – p. 19
Wave gauge 3, x = 35 m
21 22 23 24 25 26 27 28 29 30t, s
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
η, m
CFDstream function
OpenFOAM in Wave and Offshore CFD – p. 20
Dynamic Pressure Field
Sharp Dynamic Pressure Resolution Across the Free Surface
• Colour scale adjusted to show pressure variation in water and air
OpenFOAM in Wave and Offshore CFD – p. 21
Temporal Resolution Study
Varying number of time steps per wave period:
• n = 25 (coarsest temporal resolution)
• n = 50
•
.
.
.
• n = 800 (finest temporal resolution)
100 200 300 400 500 600 700 800n
4.9
5
5.1
5.2
5.3
H1 ·
10
2,
m
CFDstream function
First order amplitude
100 200 300 400 500 600 700 800n
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1
-0.9
γ H1
, m
CFDstream function
First order phase
OpenFOAM in Wave and Offshore CFD – p. 22
Mesh Refinement Study
Mesh Refinement Study
• Coarse: 2 970 cells (7.5 cells per wave height)
• Medium: 11 700 cells (15 cells per wave height)
• Fine: 46 800 cells (30 cells per wave height)
Achieved orders of accuracy
• p = 1.64 for amplitude
• p = 1.80 for phase
24 25 26 27 28 29 30t, s
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
η, m
Stream functionCoarse grid
Medium grid
Fine grid
Time Domain Signal
OpenFOAM in Wave and Offshore CFD – p. 23
Wave Reflection Study
Varying length of relaxation zone
• λr = 0.5λ
• λr = 0.75λ
•
.
.
.
• λr = 1.5λ24 25 26 27 28 29 30
t, s
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
η, m
stream function0.5λ0.75λ1λ1.25λ1.5λ
Time Domain Signal
0.5 0.75 1 1.25 1.5λ
r/λ
w (note: λ
w = 13.934 m)
4.85
4.9
4.95
5
H1 ·
10
2, m
CFDstream function
First Order Amplitude
0.5 0.75 1 1.25 1.5λ
r/λ
w (note: λ
w = 13.934 m)
-1.15
-1.1
-1.05
-1
-0.95
γ H1
, ra
d
CFDstream function
First Order Phase
OpenFOAM in Wave and Offshore CFD – p. 24
Wave Steepness Study
Wave Steepness Study Outline
• Keeping the constant wave period
• While increasing wave height
• Mesh is manipulated to always give 15 cells per wave height
• Consistency with previous simulations
◦ Same number of cells per wave height
◦ Roughly the same number of cells per wave length
• Good comparison is obtained for a simulated range of 0.045 < ka < 0.326
Note:
• Even for intermediate steepness (ka = 0.1), Benjamin–Feir instability will
eventually occur
OpenFOAM in Wave and Offshore CFD – p. 25
Wave Steepness Study, Part I
ka = 0.045
0 2 4 6 8 10 12ω, rad/s
0
0.02
0.04
0.06
0.08
0.1
|H(ω
)|
Stream functionnavalFoam
ka = 0.090
0 2 4 6 8 10 12ω, rad/s
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
|H(ω
)|
Stream functionnavalFoam
0 2 4 6 8 10 12ω, rad/s
0
0.05
0.1
0.15
0.2
0.25
0.3
|(H
ω)|
Stream functionnavalFoam
ka = 0.133
0 2 4 6 8 10 12ω, rad/s
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
|H(ω
)|
Stream functionnavalFoam
ka = 0.176
OpenFOAM in Wave and Offshore CFD – p. 26
Wave Steepness Study, Part II
ka = 0.216
0 2 4 6 8 10 12ω, rad/s
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
|H(ω
)|
Stream functionnavalFoam
ka = 0.254
0 2 4 6 8 10 12ω, rad/s
0
0.1
0.2
0.3
0.4
0.5
0.6
|H(ω
)|
Stream functionnavalFoam
0 2 4 6 8 10 12ω, rad/s
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
|H(ω
)|
Stream functionnavalFoam
ka = 0.291
0 2 4 6 8 10 12ω, rad/s
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
|H(ω
)|
Stream functionnavalFoam
ka = 0.326
OpenFOAM in Wave and Offshore CFD – p. 27
Long Simulation
Long Run Stability Assessment: 100 Wave Periods
• Testing Mass Conservation Properties of
◦ Relaxation zones
◦ Implicitly redistanced Level Set method
270 275 280 285 290 295 300t, s
-0.04
-0.02
0
0.02
0.04
0.06
η, m
Time Domain Signal
0 10 20 30 40 50 60 70 80 90 100Period index, i
0.952365
0.95237
0.952375
0.95238
0.952385
G0
Global Volume Ratio
• Negligible global conservation error: ≈ 10−4%
OpenFOAM in Wave and Offshore CFD – p. 28
Long Domain Simulation
Testing Wave Propagation in a Long Computational Domain
• Long domain simulation (approximately 8 wave lengths)
• Measured elevations at: x = 2λ, 3λ · · ·x = 6λ
2 3 4 5 6x/λ
w
4.98
4.985
4.99
4.995
5
5.005
5.01
H1 ·
10
2,
m
First Order Amplitudes
2 3 4 5 6x/λ
w
-0.05
-0.04
-0.03
-0.02
-0.01
γ H1
, ra
d
First Order Phases
OpenFOAM in Wave and Offshore CFD – p. 29
Regular Waves: Summary
Simulation of Regular Waves
• Provided guidance on spatial and temporal resolution in terms of wave height and
length
• The solver handles large cell aspect ratio without loss of accuracy
• Wave relaxation zones cause negligible reflection
• Solver is capable of preserving waves in long computational domains and for long
wave propagation time
OpenFOAM in Wave and Offshore CFD – p. 30
Irregular Wave Propagation V&V
OpenFOAM in Wave and Offshore CFD – p. 31
HOS Wave Propagation
HOS Propagation of a Non-linear Sea State
• Pseudo-spectral method: solving non-linear boundary conditions for free surfacewaves
• Truncated non-linear solution at arbitrary (user-defined) mode
• Appropriate for efficient non-linear irregular sea state propagation
• Applicable for coupling with CFD for simulation of freak wave events
• Capable of propagating a directional spectrum and generating a realistic 3D freak
wave event by screening (not tuning)
• Low CPU expense (compared to CFD): co-simulation is practical
OpenFOAM in Wave and Offshore CFD – p. 32
CFD for 3-Hour Storm Simulations
3-Hour Storm / Safe Return to Port CFD Simulation
• HOS used as input for CFD: far field relaxation zones
• SWENSE method utilised for coupling HOS and CFD
• Realised wave elevation is calibrated using HOS to correspond to the target
theoretical spectrum
• Time signal of elevation is compared between CFD and HOS
• 100 HOS and 25 CFD realisations performed altogether
0.3 0.4 0.5 0.6 0.7ω, rad/s
0
50
100
150
200
Sζζ
, m
2 s
Target: JONSWAP
HOS result after calibrationHOS result before calibration
OpenFOAM in Wave and Offshore CFD – p. 33
CFD for 3-Hour Storm Simulations
3-Hour Storm CFD
• Comparing the HOS and CFD wave spectra reveals that minimal wave damping
• Damping is related to wave spilling/breaking and vorticity effects
0.2 0.3 0.4 0.5 0.6 0.7ω, rad/s
0
50
100
150
200
Sζζ
, m
2 s
HOSCFD
OpenFOAM in Wave and Offshore CFD – p. 34
Naval Hydro Pack
Sea-Keeping, Irregular Sea States and 2-D HOS Spectrum Freak Wave
• Combining the wave modelling and sea-keeping features in a simulation of a
focused freak wave impact on a floating object: barge and full-scale KCS hull
• Freak wave has developed naturally from a 2-D spectrum without focusing
◦ Long time-series simulation of potential theory HOS model
◦ Screening wave elevation for a freak wave event
◦ Coordinate transformation for wave impact on a floating object
◦ Using HOS data to initialise CFD simulation
OpenFOAM in Wave and Offshore CFD – p. 35
Wave Diffraction V&V
OpenFOAM in Wave and Offshore CFD – p. 36
Higher Order Forces
Higher order forces on circular surface–piercing cylinder
• Important for ringing phenomenon:
◦ Wind–turbine foundations
◦ SPAR platforms
• Great validation test case since higher order effects are generally few orders of
magnitude smaller
Validation
1. All results compared to fully non–linear potential flow time–domain solution and
experiments,
2. Different wave steepnesses.
Verification
1. Time–step resolution study,
2. Mesh refinement study,
3. Periodic uncertainty (running sufficient number of periods).
Observations
• Pronounced second order behaviour of vorticity effects has been observed
OpenFOAM in Wave and Offshore CFD – p. 37
Cylinder Mesh
Mesh Statistics
• 500 000 cells
• High aspect ratio cells in far–field
OpenFOAM in Wave and Offshore CFD – p. 38
Free Surface View
OpenFOAM in Wave and Offshore CFD – p. 39
Dynamic Pressure on the Cylinder
OpenFOAM in Wave and Offshore CFD – p. 40
Higher Order Forces
• Good agreement with experiments up to: ka ≈ 0.24; periodic uncertainty error
bars
0 0.05 0.1 0.15 0.2 0.25ka
5.8
6
6.2
6.4
6.6
6.8
|F1’|
CFDEXPFerrant et al.
First order amplitudes
0 0.05 0.1 0.15 0.2 0.25ka
0
0.2
0.4
0.6
0.8
|F2’|
CFDEXPFerrant et al.
Second order amplitudes
0 0.05 0.1 0.15 0.2 0.25ka
0
0.1
0.2
0.3
0.4
|F3’|
CFDEXPFerrant et al.
Third order amplitudes
0 0.05 0.1 0.15 0.2 0.25ka
0
0.1
0.2
0.3
0.4
0.5
|F4’|
CFDEXPFerrant et al.
Fourth order amplitudes
0 0.05 0.1 0.15 0.2 0.25ka
0
0.1
0.2
0.3
0.4
0.5
|F5’|
CFDEXPFerrant et al.
Fifth order amplitudes
0.05 0.1 0.15 0.2 0.25ka
0
0.1
0.2
0.3
|F6’|
CFDEXPFerrant et al.
Sixth order amplitudes
OpenFOAM in Wave and Offshore CFD – p. 41
Time Refinement Study
Time-Step Sensitivity Study: 25 to 800 time steps per period
• Good results obtained with 100 time steps per period
• Monotonic convergence is achieved with order of accuracy between 1 and 3
(lower order of convergence for higher order effects)
100 200 300 400 500 600 700 800Number of time steps per period, n
0
0.2
0.4
0.6
0.8
Dim
ensi
on
less
fo
rce
har
mo
nic
am
pli
tud
es,
|Fi|
Normalized first order, |F1|/10
Second order, |F2|
Third order, |F3|
Fourth order, |F4|
Fifth order, |F5|
Sixth order, |F6|
Seventh order, |F7|
Convergence of force amplitudes
100 200 300 400 500 600 700 800Number of time steps per period, n
-3
-2
-1
0
1
2
3
Dim
ensi
onle
ss f
orc
e har
monic
phas
es, γ F
i, ra
d
First order, |γF
1
|
Second order, |γF
2
|
Third order, |γF
3
|
Fourth order, |γF
4
|
Fifth order, |γF
5
|
Sixth order, |γF
6
|
Seventh order, |γF
7
|
Convergence of force phases
OpenFOAM in Wave and Offshore CFD – p. 42
Mesh Refinement Study
Mesh Sensitivity Study
• Three grids: 48 600, 166 428 and 552 000 cells
• Coarse grid has only 9 cells per wave height
• Monotonic convergence is achieved with order of accuracy between 0.5 and 4
(lower order of convergence for higher order effects)
0 2 4 6 8 10t, s
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
F,
N
CoarseMediumFine
Time domain signals
1 2 3Grid index (note: 1 = coarse, 2 = medium, 3 = fine)
0
0.2
0.4
0.6
0.8
1
Dim
ensi
onle
ss f
orc
e har
monic
am
pli
tudes
, |F
i|
Normalized first order, |F1|/10
Second order, |F2|
Third order, |F3|
Fourth order, |F4|
Fifth order, |F5|
Sixth order, |F6|
Seventh order, |F7|
Convergence of force amplitudes
OpenFOAM in Wave and Offshore CFD – p. 43
Green Sea Loads
OpenFOAM in Wave and Offshore CFD – p. 44
Validation of Green Sea Loads
Simulation of Green Sea Loads
• Green sea loads simulations are extremely demanding for conventional VOF CFD
◦ Small amount of water on deck: implies high mesh resolution
◦ Any interface smearing invalidates the result: clean impact is needed for
accurate force evaluation
• Conventional Volume-of-Fluid approach smears the interface: reduced mixture
density at impact reduced pressure loads
• “Clean interface” impact is paramount: is an air pocket created or not?
• Mesh resolution requirement directly related to interface smearing
OpenFOAM in Wave and Offshore CFD – p. 45
Validation of Green Sea Loads
Green Sea Loads: Validation and Verification Study
• Green water impact pressure on deck is compared on ten locations
• Static FPSO model, 9 incident waves observed in total
• Performed complete grid and temporal resolution uncertainty study
• Experimental data from H. H. Lee, H. J. Lim & S. H. Rhee: Experimental
investigation of green water on deck for a CFD validation database (2012).
OpenFOAM in Wave and Offshore CFD – p. 46
Sharp Interface on Impact
isoAdvector Advection Preserves Sharp Interface: 1 Cell Resolution
OpenFOAM in Wave and Offshore CFD – p. 47
Green Sea Impact Pressure
Simulation of Green Sea Impact: Pressure Probes
• Pressure peaks and pressure integrals are compared,
• Numerical uncertainties = periodic + discretisation uncertainties,
• Experimental uncertainties = periodic + measuring uncertainties,
• 20 wave periods simulated to achieve periodic convergence,
• Four grid levels used: from ≈ 200 000 to ≈ 4 000 000 cells.
14 16 18 20 22 24 26Time, s
0
2000
4000
6000
8000
p,
Pa
Near the breakwater
6 8 10 12 14 16Time, s
0
100
200
300
400
500
600
700
p, P
a
Away from the breakwater
OpenFOAM in Wave and Offshore CFD – p. 48
Experimental Comparison
H = 13.5 cm, λ = 2.25 m
1 2 3 4 5 6 7 8 9 10Pressure gauge label
0
100
200
300
400
500
600
pm
ax, P
a
CFDEFD
Pressure peaks
1 2 3 4 5 6 7 8 9 10Pressure gauge label
0
50
100
150
200
250
300
P, P
a s
CFDEFD
Pressure integrals
H = 15.0 cm, λ = 3.0 m
1 2 3 4 5 6 7 8 9 10Pressure gauge label
0
100
200
300
400
500
600
700
800
pm
ax, P
a
CFDEFD
Pressure peaks
1 2 3 4 5 6 7 8 9 10Pressure gauge label
0
50
100
150
200
250
300
P, P
a s
CFDEFD
Pressure integrals
OpenFOAM in Wave and Offshore CFD – p. 49
Concluding Remarks
Naval Hydro Pack Capabilities Summary
• Regular wave propagation
• Irregular wave propagation, 3 hour storm simulation
• Wave loads – higher order forces
• Seakeeping in head and oblique waves
• Green water loads
• Full scale self propulsion
• Complete green sea load evaluation procedure for offshore structures
• Integration of mooring systems in force balance
• Full scale manoeuvring – validation in progress
• Overset grid algorithm – validation in progress
Current Work Topics
• Manoeuvring in waves and course-keeping
• Linearised free surface model: rapid manoeuvring and self propulsion simulations
OpenFOAM in Wave and Offshore CFD – p. 50