Simulation of Freak Wave Impact Using the Higher Order Spectrum

Transcription

1 Simulation of Freak Wave Impact Using the Higher Order Spectrum The Naval Hydro Pack Hrvoje Jasak and Vuko Vukčević Faculty of Mechanical Engineering and Naval Architecture, Uni Zagreb, Croatia Wikki Ltd. United Kingdom OceanFOAM Conference, Copenhagen 24 February 2016 Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 1

2 Outline Objective Demonstrate technical capabilities of the Naval Hydro Pack and FOAM-Extend in naval hydrodynamics simulations Topics Overview of the Naval Hydro Pack Decomposition method for free surface flow: relaxation zones and SWENSE Wave impact in regular sea states Freak wave simulations Higher Order Spectra (HOS) potential flow method Directional sea states Freak wave impact in irregular seas Summary Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 2

3 Naval Hydro Pack Naval Hydro Pack: Background Result of collaboration within a cluster of clients in naval hydrodynamics and wave modelling, with very similar needs. Within the Open Source framework, it makes sense to collaborate Robust surface-capturing free surface flow solver: high Co, steady formulation Dynamic mesh, 6-DOF mesh motion and mesh deformation Incoming wave conditions: regular, irregular, freak waves Prescribed forces/motion combined with 6-DOF (maneuvering, propulsion) Custom post-processing capability Tutorials, best practice guidelines Validation cases, experimental comparison Public benchmark validation workshops Naval Hydro Pack is the results of pooled developments and validation Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 3

4 Naval Hydro Pack Naval Hydro Pack: Numerics Highlights Validated second order FVM numerics with moving deforming polyhedral meshes: FOAM discretisation with improvements Choice of two-phase and mixture formulation; interface jump conditions Special steady-state formulation for rapid steady resistance and sinkage and trim studies at calm seas Time-accurate PIMPLE time-advancement for large time-step (max Co = ) Support for dynamic mesh CFD simulations, including moving deforming mesh and topological changes (Level-set solvers in incremental SWENSE formulation for sea-keeping) Naval Hydro Pack: Dynamic Mesh Prescribed harmonic graph- and function-based solid body motion Validated strongly coupled 6-DOF floating body solver Single- and multiple-body dynamic mesh classes implementing 6-DOF dynamic mesh motion and deformation 6-DOF topo motion for capsize; rigid mesh zones; combined prescribed motion and 6-DOF on individual components Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 4

5 Interface Jump Conditions Naval Hydro Pack: Interface Jump Conditions 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 Vukčević 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 dry cells, α <0.5 α =0.5 dry cell, α N <0.5 N β β + α =0.5 x Γ d f P wet cell, α P >0.5 wet cells, α >0.5 Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 5

6 Decomposition Models Decomposition Models: Wave Relaxation Zones and SWENSE General second-order CFD methodology brings a relatively high discretisation error: requirements on time-step and mesh size for realistic (irregular) wave propagation are high Introduction of sea states into a CFD domain typically cannot be done well using conventional boundary conditions: a better method is needed Relaxation Zone Approach Relaxation zones at edges of the domain are identified and the CFD solution fields are (implicitly) blended with prescribed wave fields In the bulk of the domain, conventional CFD methodology is used Domain-Wide Decomposition Approach (SWENSE) Governing equations are decomposed into the incident and diffracted (correction) component, which together make up the complete non-linear CFD solution, equivalent to solving Navier-Stokes free surface flow equations Incident fields are obtained from (complex) potential theory models CFD methodology is used to solve for the correction component Both approaches have advantages, depending on the level of non-linearity in the region of interest Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 6

7 SWENSE Solver Decomposition Models: Wave Relaxation Zones and SWENSE Conventional VOF is not appropriate for SWENSE decomposition: the Naval Hydro pack is using alternative interface capturing techniques Implicitly redistanced level set method Phase field method Modifications in implicit field blending and numerics Result: highly accurate low-cost simulations: approx. 10 times faster than conventional CFD methodology; sea-keeping approx. 100 times faster y ψ(y) = y φ(ψ) =tanh ( ψ ǫ 2 ) α(ψ) =0.5(sgn(ψ) +1) Ω 2 air Γ (0) ( 1) ( +1) (0) ( +1) x,(ψ,φ,α) water Ω 1 Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 7

8 Wave Relaxation Zones Implicit Wave Relaxation Zones Define computational domain of interest, with room for relaxation zones at inlet/outlet. Approx length of relaxation zone: wave length Relaxation zone can have arbitrary shape (cellset) with either Cartesian or cylindrical blending field 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 wavetheory and Coupling to CFD Wave forms obtained under simplified conditions satisfy the governing equation set: Blending with CFD is possible! Algorithmic issues: implicit (matrix-level) blending of u and free surface Far field mesh is coarse: sub-cell wave resolution achieved by cell cutting Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 8

9 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 Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 9

10 Mean Current Simulations Prescription of Mean Current Profile in Wave Trains In shallow seas, boundary layer at the seabed may be important Example: wave force loading on static structures rising from seabed; sediment transport driven by wave action Wave profile follows action of the wave train, with specified depth-wise profile, imposed via the relaxation zones Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 10

11 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 Mesh structure around the cylinder and free surface: high cell aspect ratio Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 11

12 Wave Impact Simulations Example: Regular Wave Impact on a Semi-Submersed Trunk Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 12

13 Wave Impact Simulations Example: Regular Wave Impact on a Semi-Submersed Trunk Comparison with experimental results: Boo Measurements of higher harmonic wave forces on a vertical truncated circular cylinder, Ocean Engineering 33 (2006) pp CFD Experimental Relative No. Courant N results results error cells number Fx, N Fx, N Err, % Co Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 13

14 Wave Impact Simulations Example: Regular Wave Impact on a Semi-Submersed Trunk Wave number study of diffraction: normalised harmonic force coefficients First to fourth order harmonics Re and Im part, comparison with Ferrant (1999) F Re(F 1 ) - CFD Im(F 1 ) - CFD F 1 - CFD Re(F 1 ) - Ferrant et al. Im(F 1 ) - Ferrant et al. F 1 - Ferrant et al kr 0.6 F Re(F 2 ) - CFD Im(F 2 ) - CFD F 2 - CFD Re(F 2 ) - Ferrant et al. Im(F 2 ) - Ferrant et al F 2 - Ferrant et al kr F 3 0 F Re(F 3 ) - CFD Im(F 3 ) - CFD F 3 - CFD Re(F 3 ) - Ferrant et al. Im(F 3 ) - Ferrant et al. F 3 - Ferrant et al Re(F 4 ) - CFD Im(F 4 ) - CFD F 4 - CFD Re(F 4 ) - Ferrant et al. Im(F 4 ) - Ferrant et al. F 4 - Ferrant et al kr kr Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 14

15 Freak Wave 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 Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 15

16 Freak Wave 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 used sea-state decomposition into amplitudes, frequencies and phase lags combined to produce a freak wave at the impact point Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 16

17 Freak Wave Simulations Freak Wave Impact on a Semi-Submersible Platform: swensefoam SWENSE-based solver is used to improve accuracy and simulation speed Equation set solved in correction form, with the basis provided by the Higher-Order Spectrum potential wave theory (implemented in FOAM) Solver accounts for all non-linear effects, including breaking waves, vorticity, turbulence, as well as higher-order non-linearity in the wave packet 8e+08 7e+08 6e+08 5e+08 F z, N 4e+08 3e+08 deck hull hull & deck 2e+08 1e e t, s Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 17

18 Higher Order Spectra Higher Order Spectra (HOS) Potential Wave Theory Higher Order Spectra (HOS) potential flow method for nonlinear surface wave propagation: pseudo spectral method for solving nonlinear free surface boundary conditions up to arbitrary order of nonlinearity The model accounts for interactions between spectral components Governing equations: dynamic and kinematic free surface conditions Solution variables: Surface velocity potential: ψ(x,y,t) = φ(x,y,z = η,t) Vertical velocity W = φ/ z ψ t +gη ( η ψ t + x, ψ ) y ( ψ x, ψ ) ( 2 1 ( η y 2 W2 1+ x, η y ( ( η x, η ) W y 1+ ) 2 ) ( η x, η ) ) 2 y = 0 = 0 Equations are integrated in space and time and used in SWENSE and wave relaxation zones: better propagation of complex wave fields Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 18

19 Higher Order Spectra Higher Order Spectra (HOS) Example: Benjamin Feir instabilities Emergence of Benjamin Feir (BF) instabilities is observed in a long time HOS propagation of monochromatic regular wave To resolve the instability, frequency interaction needs to be captured t = 0 T t = 20 T t = 200 T Modal amplitude, m 0.01 Modal amplitude, m 0.01 Modal amplitude, m ω, rad/s t = 208 T ω, rad/s t = 212 T ω, rad/s t = 216 T Modal amplitude, m 0.01 Modal amplitude, m 0.01 Modal amplitude, m ω, rad/s ω, rad/s ω, rad/s Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 19

20 Directional Sea Spectra Directional Sea Spectra Realistic sea states cannot be described using one-dimensional sea spectra: there exists a substantial scatter in directionality which needs to be accounted for Two-dimensional sea spectrum is applied and sampled as before, both in spectral components and in spreading direction Typical number of spectra/directional components is approx 600 HOS is necessary to capture the interaction between frequencies: more consistent results than in linear superposition of spectral components Short-crested and long-crested waves can be created via variation of the spectral directionality parameter m Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 20

21 Freak Wave Simulations Sea-Keeping, Irregular Sea States and 2-D 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 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 Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 21

22 Global Performance Simulations Global Performance Simulations: Work-in-Progress Software interface between native and external mooring system software established Currently, coupling with mooring system in 6-DOF solver is explicit Validation: work-in-progress by Technip-SHI-Wikki Consortium Wikki provided interface to Technip regular and irregular waves library Wikki provided interface to Technip mooring system model library Re-factoring of wave interface to accommodate expensive wave models Simplified native mooring models are available in the Naval Hydro pack Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 22

23 Summary OpenFOAM at Wikki and Uni Zagreb Substantial research activity potentially of interest in the offshore industry, only a part of which has been presented Wikki handles contracts where industrial collaboration is sought, either through support, custom development, training, process integration or collaborative simulation work Uni Zagreb has the capability of providing research support via industrial collaboration projects, funded PhD research projects or direct collaboration OpenFOAM and Open Source software infrastructure allows us to leverage existing technology and deliver custom solution to clients, by developing, implementing and validating new physical and numerical models Simulation of Freak Wave Impact Using the Higher Order Spectrum p. 23