Numerical Simulation of Wave Loads on Static Offshore Structures Hrvoje Jasak, Inno Gatin, Vuko Vukčević Wikki Ltd, United Kingdom Faculty of Mechanical Engineering and Naval Architecture University of Zagreb, Croatia h.jasak@wikki.co.uk, hrvoje.jasak@fsb.hr 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 wave generation/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 Numerical Simulation of Wave Loads on Static Offshore Structures p. 2
VOF Free Surface Flow Model Modelling of Free Surface Flows: Review of Equations Immiscible condition combines momentum equations: no inter-penetrating continua, no phase drag terms Phase continuity equation with volume fraction variable α: derived from mass conservation 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 practices available in OpenFOAM reviewed in detail Numerical Simulation of Wave Loads on Static Offshore Structures p. 3
Naval Hydro Pack Naval Hydro Pack: Summary of Capabilities While the naval hydrodynamics solvers in principle correspond to standard free surface flow formulation, for fast, robust and accurate solvers, special practices are needed 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 relaxation zones: 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 free surface and mesh deformation is used to accommodate motion of the hull Numerical Simulation of Wave Loads on Static Offshore Structures p. 4
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-trim takes 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 Numerical Simulation of Wave Loads on Static Offshore Structures p. 5
Wave Relaxation Zones Wave Relaxation Zones: Analytical Wave Forms Calculation of response to wave loading requires a wave train to be introduced into the domain with minimal distortion Wave theory derives combinations of free surface elevation and velocity field that satisfy (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 given modal frequency and significant height Number of sampling bands depends on application: typically 5 to 200 Numerical Simulation of Wave Loads on Static Offshore Structures p. 6
Wave Boundary Conditions Wave Boundary Conditions Under controlled circumstances and with sufficient mesh resolution, prescription of waves is performed at inlet boundary patches Special numerical treatment required: flow goes in-and-out, specification of free surface 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 Numerical Simulation of Wave Loads on Static Offshore Structures p. 7
Wave Boundary Conditions Example: Wave Boundary Condition Regular linear wave with zero mean velocity Numerical Simulation of Wave Loads on Static Offshore Structures p. 8
Wave Boundary Conditions Example: Wave Boundary Condition Regular linear wave at forward speed of 5 m/s Numerical Simulation of Wave Loads on Static Offshore Structures p. 9
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 Numerical Simulation of Wave Loads on Static Offshore Structures p. 10
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 following seas 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 only on boundary surface Algorithmic improvement: implicit (matrix-level) blending instead of field blending Numerical Simulation of Wave Loads on Static Offshore Structures p. 11
Wave Relaxation Zones Wave Relaxation Zones: Example of Setup Define computational domain of interest, with room for relaxation zones at inlet/outlet Relaxation zone is defined as a primitive shape, eg. rectangle or cylinder Each relaxation zone defines a wave theory model, where wave field (elevation and velocity) is obtained from analytical wave forms Across the relaxation zone, analytical and numerical solution is blended, based on a weighting function from relaxation zones In the bulk, weighting function equals zero and CFD solution is obtained Numerical Simulation of Wave Loads on Static Offshore Structures p. 12
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 Numerical Simulation of Wave Loads on Static Offshore Structures p. 13
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; sediment transport driven by wave action Wave profile follows action of the wave train, with specified depth-wise profile, imposed via the relaxation zones Numerical Simulation of Wave Loads on Static Offshore Structures p. 14
Wave Impact Simulations Example: Regular Wave Impact on a Semi-Submersed Trunk Incident wave parameters Frequency Wave height Wave length Period N f, h h, m λ, m T, s 1 0.70 0.060 3.19 1.43 2 0.70 0.120 3.19 1.43 3 0.90 0.123 1.93 1.11 4 1.10 0.050 1.30 0.90 5 1.43 0.049 0.76 0.70 Mesh stricture around the cylinder and wave relaxation zones Numerical Simulation of Wave Loads on Static Offshore Structures p. 15
Wave Impact Simulations Example: Regular Wave Impact on a Semi-Submersed Trunk Numerical Simulation of Wave Loads on Static Offshore Structures p. 16
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 number Fx, N Fx, N Err, % Co 1 1.778 1.80 1.22 1 728 490 6.0 2 4.790 5.00 4.20 1 728 490 6.0 3 5.573 5.70 2.23 1 728 490 2.0 4 2.390 2.80 14.64 1 728 490 1.5 4 2.361 2.80 15.68 2 805 810 1.5 5 2.650 3.08 13.96 1 728 490 2.0 5 2.854 3.08 7.34 2 629 410 2.0 Numerical Simulation of Wave Loads on Static Offshore Structures p. 17
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 in time-space 30 harmonic wave components Phase shifts for individual wave components set up using optimisation Sea spectrum significant height h s = 0.12m Optimisation achieves freak wave height H = 0.28 m Domain layout and mesh identical to wave train simulation Numerical Simulation of Wave Loads on Static Offshore Structures p. 18
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 and phase lags required to produce the freak wave at point of impact Numerical Simulation of Wave Loads on Static Offshore Structures p. 19
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 Numerical Simulation of Wave Loads on Static Offshore Structures p. 20
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 of generating waves on a coarse (far field) mesh Support for mean current/forward boat speed and depth-wise current boundary layer profiles in shallow seas Implementation of freak wave conditions by prescribed superposition Wave boundary conditions integrated with navalfoam solvers, with support for dynamic mesh motion Numerical Simulation of Wave Loads on Static Offshore Structures p. 21