Numerical Simulation of Wave Loads on Static Offshore Structures

Numerical Simulation of Wave Loads onStatic Offshore Structures

Hrvoje Jasak, Inno Gatin, Vuko Vuk cevi c

Wikki Ltd, United Kingdom

Faculty of Mechanical Engineering and Naval Architecture

University of Zagreb, Croatia

[email protected], [email protected]

Water Waves Theories and the Marine Industries Workshop, Cambridge, 30 July 2014

Numerical Simulation of Wave Loads on Static Offshore Structures – p. 1

Outline

Objective

• Describe capabilities and implementation of wave boundary conditions and wavegeneration/relaxation zones in the Naval Hydro Pack

Topics

1. Introduction: Naval Hydro Pack for hydrodynamics simulations

2. Wave forms

3. Wave boundary conditions

4. Wave theory and relaxation zones

5. Example: wave loading simulations

6. Example: freak wave simulation

7. Summary


VOF Free Surface Flow Model

Modelling of Free Surface Flows: Review of Equations

• Immiscible condition combines momentum equations: no inter-penetratingcontinua, no phase drag terms

• Phase continuity equation with volume fraction variable α: derived from massconservation for a phase

∂α

∂t+∇•(uα) = 0

• Combined momentum equation

∂(ρu)

∂t+∇•(ρuu)−∇•σ = −∇p+ ρf

• Volumetric continuity equation, to be reformulated in terms of pressure

∇•u = 0

• Discretisation issues arising from the above will be investigated and practicesavailable in OpenFOAM reviewed in detail


Naval Hydro Pack

Naval Hydro Pack: Summary of Capabilities

• While the naval hydrodynamics solvers in principle correspond to “standard” freesurface flow formulation, for fast, robust and accurate solvers, special practices areneeded

• VoF equation: compressive numerics, relative velocity formulation and MULES

• 2 variants of formulation of the momentum equation

• Factorisation and reconstruction of the pressure field

• Numerical damping of VOF, pressure and momentum equation within relaxationzones: blending with regions where wave shape is prescribed

• Sub-cell resolution of prescribed wave forms in relaxation zones

• Support for dynamic mesh with 6-DOF solver mesh motion classes

◦ Domain motion: complete mesh moves with the motion of the hull

◦ Mesh deformation: far field mesh remains aligned with the flow and freesurface and mesh deformation is used to accommodate motion of the hull


Naval Hydro Pack

Naval Hydro Pack: Custom Solver Capability

• The main issue in most cases is speed of execution:

◦ Large domain and large Re number with fine near-wall resolution

◦ Intrinsic limitation of free surface tracking to the speed of interface motion

◦ Achieving steady-state solution for steady resistance or sinkage-and-trimtakes a very long time

• For transient runs, global time-step size needs to be physically realistic:sea-keeping simulations with a time step of 1/1000 second are pointless!

• With the Naval Hydro pack, Co number is not a factor: realistic time-step size (0.1 -2 second, depending on model size)

Naval Hydro Solvers

• Co number-tolerant transient solvers◦ navalFoam. Max Co number well over 8000

• Specialist steady-state formulation◦ steadyNavalFoam


Wave Relaxation Zones

Wave Relaxation Zones: Analytical Wave Forms

• Calculation of response to wave loading requires a wave train to be introduced intothe domain with minimal distortion

• Wave theory derives combinations of free surface elevation and velocity field thatsatisfy (simplified forms of) the free surface flow equation set

• Implemented wave forms: from waves2Foam by Dr. Niels Gjoel Jacobsen, DTU(Int.J.Num.Meth.Fluids, 2011)

◦ Potential current (“numerical beach”)

◦ Solitary wave◦ Regular waves

∗ Linear wave (first order Stokes wave)∗ First, second and fifth order Stokes standing wave∗ Cnoidal wave

◦ Irregular waves, prescribed harmonics: freak wave simulations◦ Irregular waves: Bretschneider sea state wave spectrum

∗ Superposition of linear waves to reproduce random behaviour with givenmodal frequency and significant height

∗ Number of sampling bands depends on application: typically 5 to 200


Wave Boundary Conditions


• Under controlled circumstances and with sufficient mesh resolution, prescription ofwaves is performed at inlet boundary patches

• Special numerical treatment required: flow goes in-and-out, specification of freesurface elevation is not trivial

• Current implementation does not allow for sub-cell resolution of incoming wave

• Consistency in α and U boundary condition is paramount!

Implemented Wave Boundary Conditions

• Water table boundary: constant free surface level on a moving mesh

• Linear wave

• Waves with forward speed (eg. ship on waves simulations)

• Bretschneider sea state wave spectrum



Example: Wave Boundary Condition

• Regular linear wave with zero mean velocity




• Regular linear wave at forward speed of 5 m/s




• Irregular Bretschneider sea state spectrum at forward speed of 5 m/s

• Significant height = 3.3 m; modal frequency = 0.64 Hz, n bands = 10




• Under some circumstances, wave boundary conditions are inappropriate:

◦ Far field mesh is coarse: sub-cell wave resolution required◦ Moving and pitching inlet boundary: no longer possible to impose a 1-D

vertical solution◦ High fidelity required: introduce wave train with minimum distortion

◦ Cases with badly posed flow conditions, eg. ship at forward speed in followingseas

◦ Numerical beach relaxation in cases with forwards speed

• Jacobsen approach: DTU Copenhagen◦ Wave forms obtained under simplified conditions satisfy the governing

equation set◦ It is therefore possible to blend numerical solution in the bulk with analytical

wave prescription in relaxation regions

◦ Analytical wave trains are now specified in the volume , as opposed to onlyon boundary surface

• Algorithmic improvement: implicit (matrix-level) blending instead of field blending



Wave Relaxation Zones: Example of Setup

• Define computational domain of interest, with room for relaxation zones atinlet/outlet

• Relaxation zone is defined as a primitive shape, eg. rectangle or cylinder

• Each relaxation zone defines a wave theory model, where wave field (elevationand velocity) is obtained from analytical wave forms

• Across the relaxation zone, analytical and numerical solution is blended, based ona weighting function from relaxation zones

• In the bulk, weighting function equals zero and CFD solution is obtained



Example: Wave Generator and Potential Current

• Inlet wave relaxation zone: regular Stokes waves with soft ramp time

• Outlet relaxation zone: potential current, fixed water table


Mean Current Simulations

Prescription of Mean Current Profile in Wave Trains

• In shallow seas, boundary layer at the sea bead may be important

• Example: wave force loading on static structures rising from sea bead; sedimenttransport driven by wave action

• Wave profile follows action of the wave train, with specified depth-wise profile,imposed via the relaxation zones


Wave Impact Simulations

Example: Regular Wave Impact on a Semi-Submersed Trunk

• Incident wave parameters

Frequency Wave height Wave length PeriodN f, h h, m λ, m T, s

1 0.70 0.060 3.19 1.432 0.70 0.120 3.19 1.433 0.90 0.123 1.93 1.114 1.10 0.050 1.30 0.905 1.43 0.049 0.76 0.70

• Mesh stricture around the cylinder and wave relaxation zones




• Comparison with experimental results

CFD Experimental Relative No. Courant

N results results error cells numberFx , N Fx , N Err, % Co

1 1.778 1.80 1.22 1 728 490 6.02 4.790 5.00 4.20 1 728 490 6.03 5.573 5.70 2.23 1 728 490 2.04 2.390 2.80 14.64 1 728 490 1.54 2.361 2.80 15.68 2 805 810 1.55 2.650 3.08 13.96 1 728 490 2.05 2.854 3.08 7.34 2 629 410 2.0



Example: Freak Wave Impact on a Semi-Submersed Trunk

• Wave components correspond to the Pierson-Moskowitz sea energy spectrum

• Wave focusing method was used to create a freak wave at a given point intime-space◦ 30 harmonic wave components

◦ Phase shifts for individual wave components set up using optimisation

◦ Sea spectrum significant height hs = 0.12m

◦ Optimisation achieves freak wave height H = 0.28m

• Domain layout and mesh identical to wave train simulation



Example: Freak Wave Impact on a Semi-Submersed Trunk

• Characteristics of a desired freak wave prescribed at the point of impact

• Freak wave model describes decomposition into amplitudes, frequencies andphase lags required to produce the freak wave at point of impact


6-DOF Wave Simulations

Example: Wave Simulations with Fixed and Moving Hulls

• Simulations of static and (6-DOF hulls in waves with or without forward speed

• Mesh size: 582k cells, 9 wave impacts simulated in 17 hrs on 1 CPU


Summary

Summary

• Naval Hydro Pack is equipped with wave maker conditions◦ Patch-based conditions◦ Relaxation zone conditions

• Number of wave forms available for run-time selection

• Relaxation zone conditions provide sub-cell wave resolution: possibility ofgenerating waves on a coarse (far field) mesh

• Support for mean current/forward boat speed and depth-wise current boundarylayer profiles in shallow seas

• Implementation of freak wave conditions by prescribed superposition

• Wave boundary conditions integrated with navalFoam solvers, with support fordynamic mesh motion


Numerical Simulation of Wave Loads on Static Offshore Structures

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