openfoam in wave and offshore cfd - foam-extend.fsb.hr · ghost ﬂuid method for accurate...

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


Ghost Fluid Method

N

dry cell, ψN <0

P

wet cell, ψP >0

ψ=0β−

β+

df

xΓ


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


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


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.


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


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


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


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.


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


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



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


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


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


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


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)


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


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


Dynamic Pressure Field

Sharp Dynamic Pressure Resolution Across the Free Surface

• Colour scale adjusted to show pressure variation in water and air


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


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


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


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


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

)|


0 2 4 6 8 10 12ω, rad/s

0

0.05

0.1

0.15

0.2

0.25

0.3

|(H

ω)|


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

)|


ka = 0.176


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

)|


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

)|


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

)|


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

)|


ka = 0.326


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%


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


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


Irregular Wave Propagation V&V


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


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


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


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


Wave Diffraction V&V


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


Cylinder Mesh

Mesh Statistics

• 500 000 cells

• High aspect ratio cells in far–field


Free Surface View


Dynamic Pressure on the Cylinder


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’|


Second order amplitudes

0 0.05 0.1 0.15 0.2 0.25ka

0

0.1

0.2

0.3

0.4

|F3’|


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’|


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’|


Fifth order amplitudes

0.05 0.1 0.15 0.2 0.25ka

0

0.1

0.2

0.3

|F6’|


Sixth order amplitudes


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



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


Green Sea Loads


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


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).


Sharp Interface on Impact

isoAdvector Advection Preserves Sharp Interface: 1 Cell Resolution


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


figures/greenSea/wave9PressureP11.png

figures/greenSea/wave9PressureP31.png

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


0

50

100

150

200

250

300

P, P

a s

CFDEFD

Pressure integrals

H = 15.0 cm, λ = 3.0 m


0

100

200

300

400

500

600

700

800

pm

ax, P

a

CFDEFD

Pressure peaks


0

50

100

150

200

250

300

P, P

a s

CFDEFD

Pressure integrals


figures/greenSea/wave3ResultsPeaks.eps

figures/greenSea/wave3ResultsIntegral.eps



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 - foam-extend.fsb.hr · ghost ﬂuid method for accurate...

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