OpenFOAM in Wave and Offshore CFD

Transcription

1 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 217 OpenFOAM in Wave and Offshore CFD p. 1

2 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 OpenFOAM in Wave and Offshore CFD p. 2

3 Ghost Fluid Method dry cell, ψ N < N β β + ψ = x Γ d f P wet cell, ψ P > OpenFOAM in Wave and Offshore CFD p. 3

4 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. (27) 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 (215) 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 <.5 α =.5 dry cell, ψ N < N β β + ψ = x Γ d f P wet cell, ψ P > wet cells, α >.5 OpenFOAM in Wave and Offshore CFD p. 4

5 Ghost Fluid Method Interface Jump Conditions: Derivation Conditionally averaged momentum equation: (ρu) t + (ρuu) = σ eff p d (g x ρ) ρ and p d have a jump across the free surface Taking derivatives of discontinuous fields Looking at the rhs of the equation, the gradient of dynamic pressure ( p d ) is balanced by the density gradient ( ρ) The ρ-p d 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 OpenFOAM in Wave and Offshore CFD p. 5

6 Ghost Fluid Method Ordinary Interpolation is Insufficiently Accurate: Incorrect Gradients φ φ P P : cell centre, N: cell centre, φ f f: face centre, Γ f : interface. φ N P Γ f f N x OpenFOAM in Wave and Offshore CFD p. 6

7 Ghost Fluid Method Interface Jump Conditions: Derivation "Mixture formulation" of the momentum equation: u t + (uu) (ν e u) = 1 ρ p d Dynamic pressure jump conditions at the interface: [p d ] = [ρ]g x [ ] 1 ρ p d = 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 OpenFOAM in Wave and Offshore CFD p. 7

8 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 With the following governing equations 1 ρ + p+ d 1 ρ p d = u = u t + (uu) (ν e u) = 1 ρ p d Pressure density coupling moved from the momentum equation to the pressure equation OpenFOAM in Wave and Offshore CFD p. 8

9 Ghost Fluid Method Interpolation uses extrapolated ("ghost") values, yielding correct gradients dry cell, ψ N < N β β + ψ = Cell P and N share an interface face, x Γ P d f x Γ is the location of the interface for this pair of dry/wet cells wet cell, ψ P > OpenFOAM in Wave and Offshore CFD p. 9

10 Ghost Fluid Method The Ghost Fluid Method with Compact Stencil Support φ φ P φ + φ + f φ + N : extrapolated value at cell centre N, φ + N φ P : extrapolated value at cell centre P, φ P φ φ f φ N φ +, f : face values via GFM interpolation. P Γ f f N x OpenFOAM in Wave and Offshore CFD p. 1

11 Interface Jump Conditions Interface Jump Conditions: Results Example: 2D ramp with free surface Relative error for water height at the outlet is.34% compared to analytical solution Note sharp p d jump and α distribution The simulation withinterfoam is not stable due to spurious air velocities OpenFOAM in Wave and Offshore CFD p. 11

12 Geometric Free Surface Advection OpenFOAM in Wave and Offshore CFD p. 12

13 Geometric Free Surface Advection isoadvector: Accurate Free Surface Convection via 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 reconstruction technique based on exact face flux and iso-surface reconstruction OpenFOAM in Wave and Offshore CFD p. 13

14 Geometric Free Surface Advection Geometric Reconstruction with theisoadvector 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 OpenFOAM in Wave and Offshore CFD p. 14

15 Regular Wave Propagation V&V.8.6 CFD stream function.4.2 η, m t, s OpenFOAM in Wave and Offshore CFD p. 15

16 Wave Propagation Tests Benchmark Case: Regular Waves Domain for wave propagation: 6m x 6.3m Stream function wave: H =.1m, T = 3s, d = 6m Mild steepness, ka.225 Approximately 4 wave lengths in the domain 1 wave periods were simulated Coarse, heavily graded mesh towards the area of interest 11 7 cells, maximum aspect ratio is 213:1 High aspect ratio is not an issue OpenFOAM in Wave and Offshore CFD p. 16

17 Computational Mesh Zoomed View in the Middle Region: Wave Action High aspect ratio cells Approx 1 cells per wave length Approx 15 cells per wave height OpenFOAM in Wave and Offshore CFD p. 17

18 Weight (Blending) Field Weight Field: Far Field Relaxation Zones Exponential function (w = 1 at the boundary and in the patch cells) Top figure: w = (1% of the CFD solution) Middle figure: < w <.5 (at least 5% CFD solution) Bottom figure: < w < 1 (whole domain) OpenFOAM in Wave and Offshore CFD p. 18

19 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 OpenFOAM in Wave and Offshore CFD p. 19

20 Wave gauge 3, x = 35 m.8.6 CFD stream function.4.2 η, m t, s OpenFOAM in Wave and Offshore CFD p. 2

21 Dynamic Pressure Field Sharp Dynamic Pressure Resolution Across the Free Surface Colour scale adjusted to show pressure variation in water and air OpenFOAM in Wave and Offshore CFD p. 21

22 Temporal Resolution Study Varying number of time steps per wave period: n = 25 (coarsest temporal resolution) n = 5. n = 8 (finest temporal resolution) CFD stream function CFD stream function H 1 1 2, m 5.1 γ H1, m n First order amplitude n First order phase OpenFOAM in Wave and Offshore CFD p. 22

23 Mesh Refinement Study Mesh Refinement Study Coarse: 2 97 cells (7.5 cells per wave height) Medium: 11 7 cells (15 cells per wave height) Fine: 46 8 cells (3 cells per wave height) Stream function Coarse grid Medium grid Fine grid Achieved orders of accuracy p = 1.64 for amplitude p = 1.8 for phase η, m t, s Time Domain Signal OpenFOAM in Wave and Offshore CFD p. 23

24 Wave Reflection Study Varying length of relaxation zone λ r =.5λ λ r =.75λ. η, m stream function.5λ.75λ 1λ 1.25λ 1.5λ λ r = 1.5λ t, s Time Domain Signal CFD stream function CFD stream function H 1 1 2, m 4.9 γ H1, rad λ r /λ w (note: λ w = m) First Order Amplitude λ r /λ w (note: λ w = m) First Order Phase OpenFOAM in Wave and Offshore CFD p. 24

25 Wave Steepness Study Wave Steepness Study Outline Note: 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.45 < ka <.326 Even for intermediate steepness (ka =.1), Benjamin Feir instability will eventually occur OpenFOAM in Wave and Offshore CFD p. 25

26 Wave Steepness Study, Part I.1 ka =.45.2 ka =.9.8 Stream function navalfoam Stream function navalfoam H(ω) H(ω) ω, rad/s ω, rad/s.4.25 Stream function navalfoam.35 Stream function navalfoam (Hω).15 H(ω) ω, rad/s ka = ω, rad/s ka =.176 OpenFOAM in Wave and Offshore CFD p. 26

27 Wave Steepness Study, Part II.5 ka = ka = Stream function navalfoam.5 Stream function navalfoam H(ω).25 H(ω) ω, rad/s ω, rad/s Stream function navalfoam.7 Stream function navalfoam H(ω).3 H(ω) ω, rad/s ka = ω, rad/s ka =.326 OpenFOAM in Wave and Offshore CFD p. 27

28 Long Simulation Long Run Stability Assessment: 1 Wave Periods Testing Mass Conservation Properties of Relaxation zones Implicitly redistanced Level Set method G η, m t, s Time Domain Signal Period index, i Global Volume Ratio Negligible global conservation error: 1 4 % OpenFOAM in Wave and Offshore CFD p. 28

29 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 H 1 1 2, m γ H1, rad x/λ w First Order Amplitudes x/λ w First Order Phases OpenFOAM in Wave and Offshore CFD p. 29

30 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 OpenFOAM in Wave and Offshore CFD p. 3

31 Irregular Wave Propagation V&V OpenFOAM in Wave and Offshore CFD p. 31

32 HOS Wave Propagation HOS Propagation of a Non-linear Sea State Pseudo-spectral method: solving non-linear boundary conditions for free surface waves 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 OpenFOAM in Wave and Offshore CFD p. 32

33 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 1 HOS and 25 CFD realisations performed altogether 2 15 Target: JONSWAP HOS result after calibration HOS result before calibration S ζζ, m 2 s ω, rad/s OpenFOAM in Wave and Offshore CFD p. 33

34 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 2 15 HOS CFD S ζζ, m 2 s ω, rad/s OpenFOAM in Wave and Offshore CFD p. 34

35 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 OpenFOAM in Wave and Offshore CFD p. 35

36 Wave Diffraction V&V OpenFOAM in Wave and Offshore CFD p. 36

37 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 OpenFOAM in Wave and Offshore CFD p. 37

38 Cylinder Mesh Mesh Statistics 5 cells High aspect ratio cells in far field OpenFOAM in Wave and Offshore CFD p. 38

39 Free Surface View OpenFOAM in Wave and Offshore CFD p. 39

40 Dynamic Pressure on the Cylinder OpenFOAM in Wave and Offshore CFD p. 4

41 Higher Order Forces Good agreement with experiments up to: ka.24; periodic uncertainty error bars F 1 F 3 F CFD EXP Ferrant et al ka First order amplitudes ka CFD EXP Ferrant et al. Third order amplitudes CFD EXP Ferrant et al ka Fifth order amplitudes F 2 F 4 F CFD EXP Ferrant et al ka Second order amplitudes CFD EXP Ferrant et al ka Fourth order amplitudes CFD EXP Ferrant et al ka Sixth order amplitudes OpenFOAM in Wave and Offshore CFD p. 41

42 Time Refinement Study Time-Step Sensitivity Study: 25 to 8 time steps per period Good results obtained with 1 time steps per period Monotonic convergence is achieved with order of accuracy between 1 and 3 (lower order of convergence for higher order effects).8 3 Dimensionless force harmonic amplitudes, F i Normalized first order, F 1 /1 Second order, F 2 Third order, F 3 Fourth order, F 4 Fifth order, F 5 Sixth order, F 6 Seventh order, F 7 Dimensionless force harmonic phases, γ Fi, rad First order, γ F1 Second order, γ F2 Third order, γ F3 Fourth order, γ F4 Fifth order, γ F5 Sixth order, γ F6 Seventh order, γ F Number of time steps per period, n Convergence of force amplitudes Number of time steps per period, n Convergence of force phases OpenFOAM in Wave and Offshore CFD p. 42

43 Mesh Refinement Study Mesh Sensitivity Study Three grids: 48 6, and 552 cells Coarse grid has only 9 cells per wave height Monotonic convergence is achieved with order of accuracy between.5 and 4 (lower order of convergence for higher order effects) 1 1 F, N Coarse Medium Fine Dimensionless force harmonic amplitudes, F i Normalized first order, F 1 /1 Second order, F 2 Third order, F 3 Fourth order, F 4 Fifth order, F 5 Sixth order, F 6 Seventh order, F t, s Time domain signals Grid index (note: 1 = coarse, 2 = medium, 3 = fine) Convergence of force amplitudes OpenFOAM in Wave and Offshore CFD p. 43

44 Green Sea Loads OpenFOAM in Wave and Offshore CFD p. 44

45 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 OpenFOAM in Wave and Offshore CFD p. 45

46 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 (212). OpenFOAM in Wave and Offshore CFD p. 46

47 Sharp Interface on Impact isoadvector Advection Preserves Sharp Interface: 1 Cell Resolution OpenFOAM in Wave and Offshore CFD p. 47

48 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, 2 wave periods simulated to achieve periodic convergence, Four grid levels used: from 2 to 4 cells p, Pa p, Pa Time, s Near the breakwater Time, s Away from the breakwater OpenFOAM in Wave and Offshore CFD p. 48

49 Experimental Comparison 6 5 H = 13.5 cm, λ = 2.25 m CFD EFD 8 7 H = 15. cm, λ = 3. m CFD EFD p max, Pa p max, Pa Pressure gauge label Pressure gauge label Pressure peaks Pressure peaks 3 25 CFD EFD 3 25 CFD EFD P, Pa s 2 15 P, Pa s Pressure gauge label Pressure integrals Pressure gauge label Pressure integrals OpenFOAM in Wave and Offshore CFD p. 49

50 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 p. 5