Numerical Simulation of Wave Loads on Static Offshore Structures · 2016. 8. 3. · Numerical...
Transcript of Numerical Simulation of Wave Loads on Static Offshore Structures · 2016. 8. 3. · Numerical...
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
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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
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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
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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
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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
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Wave Boundary Conditions
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
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Wave Boundary Conditions
Example: Wave Boundary Condition
• Regular linear wave with zero mean velocity
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Wave Boundary Conditions
Example: Wave Boundary Condition
• Regular linear wave at forward speed of 5 m/s
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Wave Boundary Conditions
Example: Wave Boundary Condition
• 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
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Wave Relaxation Zones
Wave Relaxation Zones
• 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
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Wave Relaxation Zones
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
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Wave Relaxation Zones
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
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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
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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
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Wave Impact Simulations
Example: Regular Wave Impact on a Semi-Submersed Trunk
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Wave Impact Simulations
Example: Regular Wave Impact on a Semi-Submersed Trunk
• 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
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Wave Impact Simulations
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
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Wave Impact Simulations
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
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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
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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
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