FROTH: Fundamentals and Reliability of

Transcription

1 FROTH: Fundamentals and Reliability of Offshore structure Hydrodynamics EPSRC

2 Wave Directionality, Wave Impact and Response of Floating Bodies in Extreme Sea WP3 (City) Qingwei Ma & Shiqiang Yan School of Mathematics, Computer Science & Engineering, City University London WP1(PU) Tri Mai, Deborah Greaves & Alison Raby School of Marine Science and Engineering Plymouth University WP5(UoB) Feng Gao & Jun Zang Department of Architecture and Civil Engineering, University of Bath

3 Reality at start of this project Highly nonlinear wave condition Large sea area ~ 100km 2 (10sλ 10sλ) Multiple-wave systems, not unidirectional or single wave groups Wave impact and viscosity may play important role Uncertainties and Challenges How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? How reliable are numerical results obtained by using existing nonlinear models? How to efficiently model the wave impact and motion response of floating bodies in extreme sea? Linear theory & approach, Stokes or other nonlinear wave theories is not sufficient for extreme seas; Fully nonlinear potential theory ignoring viscos effects; CFD packages based on viscous model take too long WP3: Wave directionality and motion response of floating bodies (City) WP1: FPSO model tests (PU) WP5: Reliability of wave impact pressure prediction (UoB) 10/11/2016 FROTH Workshop 18 November

4 FPSO Model Test at PU Objectives: to investigate experimentally: Wave impact on a fixed and/or free floating FPSO model under various focused wave groups of different steepness, directionality, and different relative position (phase) between the model and the highest directional wave crest. Wave scattering around different lengths of FPSO model. Behaviour of model constrained in heave only or in heave & pitch. Model 1 Model 2 Model 3 10/11/2016 FROTH Workshop 18 November

5 FPSO Test: Layout of WGs & Pressure Sensor Plymouth wave basin: Length: 35 m Width: 15.5m Mean water depth (d): 2.93m Focusing location: m from the wavemaker 10/11/2016 FROTH Workshop 18 November

6 How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? A general phase-based harmonic separation method (Fitzgerald et al., 2012) Extreme Waves without structures Physical Modelling at Plymouth University Time histories of wave elevation at focused location (model test by Plymouth University) Separate linear, 2 nd -order, 3 rd -order and 4 th -order harmonics using groups of model tests 10/11/2016 FROTH Workshop 18 November

7 Extreme Waves without structures Physical Modelling at Plymouth University How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? Amplitude spectra of separated components at the focus location(model test by Plymouth University) Insignificant 2 nd -order (~6%) and higher order harmonics Time series of separated components at the focus location (model test by Plymouth University) 10/11/2016 FROTH Workshop 18 November

8 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? Same weekly nonlinear wave, but a different story if structures are involved Investigate the significance of the nonlinearity considering WG10 WG4 WG8 WG WG10 Effects of structure geometry (FPSO length) 3 FPSO models Ka = 0.21 WG10 WG7 10/11/2016 FROTH Workshop 18 November WG22 Effects of wave steepness: FPSO model M3, Ka = 0.13 and 0.18) WG7 Effects of wave obliqueness: FPSO model M3, 0~20 0 )

9 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? - effects of FPSO length Comparison of amplitude spectra of separated components at WG10 near the bow (model test by Plymouth University, same relative position to the bow of FPSO) Significance of the nonlinearity is considerably influenced by the length of FPSO 10/11/2016 FROTH Workshop 18 November

10 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University Model 1 (shortest length) has the highest amplitude scattered waves. The 2 nd harmonic scattered wave field is comparable in amplitude to the incident bound waves. The 3 rd and 4 th order harmonic scattered wave field is significantly larger than the incident bound component. Comparison of time histories (incident and scattered waves) of separated components at WG10 near the bow (model test by Plymouth University) 10/11/2016 FROTH Workshop 18 November

11 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University Model 1 (shortest length) has the highest amplitude scattered waves. The 2 nd harmonic scattered wave field is comparable in amplitude to the incident bound waves. The 3 rd and 4 th order harmonic scattered wave field is significantly larger than the incident bound component. Comparison of time histories (scattered waves only) of separated components at WG10 near the bow (model test by Plymouth University) 10/11/2016 FROTH Workshop 18 November

12 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? - effects of FPSO length Comparison of amplitude spectra of separated components at WG10 near the Stern (model test by Plymouth University, same relative position to the stern of FPSO) WG4 WG8 WG22 10/11/2016 FROTH Workshop 18 November

13 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University The linear harmonic increases as model length decreases. The non-linear harmonics are similar in amplitude for all 3 models, but slightly smaller for model 3 in the 2 nd order component. Comparison of time histories (incident and scattered waves) of separated components at WG10 near the stern (model test by Plymouth University) 10/11/2016 FROTH Workshop 18 November

14 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University Comparison of time histories (scattered waves only) near the stern Model M1 Model M2 Model M3 10/11/2016 FROTH Workshop 18 November

15 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? - effects of Wave Steepness Comparison of amplitude spectra of separated components at WG10 near the bow(model test by Plymouth University) Nonlinearity increases as wave steepness increases WG10 10/11/2016 FROTH Workshop 18 November

16 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? - effects of Wave Steepness Comparison of amplitude spectra of separated components at WG7 alongside (model test by Plymouth University) Nonlinearity increases as wave steepness increases WG7 10/11/2016 FROTH Workshop 18 November

17 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? - effects of Wave Steepness Comparison of amplitude spectra of separated components at WG22 near the stern(model test by Plymouth University) Nonlinearity increases as wave steepness increases WG22 10/11/2016 FROTH Workshop 18 November

18 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? - effects of Wave Obliqueness Comparison of amplitude spectra of separated components at WG10 near the bow (model test by Plymouth University) Nonlinearity is the most significant when the incident angle is 10deg WG10 10/11/2016 FROTH Workshop 18 November

19 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University The 2 nd order scattered waves are greatest for wave angle of 10 deg. The 4 th order scattered waves reduce as wave angle increases from 0 to 20 deg. Similar conclusions drawn for wave elevations at other area WG10 Comparison of time histories (scattered waves only) of separated components at WG10 near the bow (model test by Plymouth University) 10/11/2016 FROTH Workshop 18 November

20 Extreme Waves With Fixed FPSO Models Physical Modelling at Plymouth University Effect of model length: Bow: Model 1 has the highest amplitude scattered waves. The 2 nd harmonic scattered wave field is comparable in amplitude to the incident bound waves, whereas the 3 rd and 4 th order harmonic scattered wave field is significantly larger than the incident bound component. Stern: The linear harmonic increases as model length decreases. The nonlinear harmonics are similar in amplitude for all 3 models, but slightly smaller for model 3 in the 2 nd order component. Effect of steepness: The non-linear scattered wave increases with wave steepness. A second pulse is evident in the higher order scattered wave fields. Effect of wave angle: The 2 nd order scattered waves are greatest for wave angle of 10 deg. The 4 th order scattered waves reduce as wave angle increases from 0 to 20 deg. Linear and 2 nd order wave diffraction analysis are not sufficient 10/11/2016 FROTH Workshop 18 November

21 (m) Extreme Waves without structures Numerical Modelling at City: Self-Correction Wavemaker How reliable are numerical results obtained by using existing nonlinear models? Can we accurately reproduce extreme waves in numerical tanks? experimental Flap wavemaker(linear):ds=0.02m Flap wavemaker(linear):ds=0.015m Piston wavemaker(2nd order):ds=0.02m Piston wavemaker(2nd order):ds=0.015m time(s) Time series of separated components at the focus location (Numerical results by City) Inconsistence between the experimental measurement and numerical solutions using linear or 2 nd order wavemaker theory, flap or piston wavemaker -- Not because of the accuracy of the numerical model -- Mainly due to uncertainties Even for lab test data, it is difficult to accurately reproduce extreme waves based on specific gauge data Common in reality: only the time history of wave elevation at a specific location may be measured 10/11/2016 FROTH Workshop 18 November

22 Extreme Waves without structures Numerical Modelling at City: Self-Correction Wavemaker How reliable are numerical results obtained by using existing nonlinear models? (m) experimental Flap wavemaker(linear):ds=0.02m Flap wavemaker(linear):ds=0.015m Piston wavemaker(2nd order):ds=0.02m Piston wavemaker(2nd order):ds=0.015m time(s) Time series of separated components at the focus location (Numerical results by City) Inconsistence between the experimental measurement and numerical solutions using linear or 2 nd order wavemaker theory, flap or piston wavemaker -- Not because of the accuracy of the numerical model -- Mainly due to uncertainties Iteration to correct the amplitude and phase of each wave components Either linear or 2 nd order wavemaker theory To generate random/focusing wave using the observed data Further development to overcome the problem of inconsistent sampling frequency between experiment and numerical work Self-correction Wavemaker (2 nd order) 10/11/2016 FROTH Workshop 18 November

23 (m) How reliable are numerical results obtained by using existing nonlinear models? amplitude spectrum (m) experimental phase only phase and amplitude time(s) 4 x experimental phase only phase and amplitude f(hz) Extreme Waves without structures Numerical Modelling at City: Self-Correction Wavemaker Both the wave elevation and the spectrum obtained at the targeted location agree well with the measurement Correcting phase only and phase plus amplitude both seem to delivery promising results The wave elevations obtained at different iterative steps during self-correction based on the gauge data at WG1(12.391m from the wave paddle, significant wave height 0.103m). 10/11/2016 FROTH Workshop 18 November

24 Extreme Waves without structures Numerical Modelling at City: Self-Correction Wavemaker How reliable are numerical results obtained by using existing nonlinear models? Good agreements achieved not only at the location where the data is used for the correction not also at other locations (m) QALE-FEM exp (a) WG11 (m) QALE-FEM exp (d) WG18 (m) time(s) (b) WG QALE-FEM exp 0 (m) time(s) (e) WG QALE-FEM exp 0 (m) (c) time(s) WG QALE-FEM exp 0 (m) time(s) (f) WG QALE-FEM exp time(s) time(s) The wave elevations obtained at different gauges(significant wave height 0.103m). 10/11/2016 FROTH Workshop 18 November

25 Extreme Waves With Fixed FPSO Models Numerical Modelling (City, PU and UoB) How reliable are numerical results obtained by using existing nonlinear models? Adopt two approaches, Fully Nonlinear Potential Theory (QALE-FEM at City) City General Flow Theory (Open Foam at PU and UoB) To investigate their reliability on modelling FPSO in extreme sea UoB 10/11/2016 FROTH Workshop 18 November

26 Extreme Waves With Fixed FPSO Models Reliability of QALE-FEM at City How reliable are fully nonlinear predictions on wave elevations near fixed FPSO? FNPT model (QALE-FEM): Model 3, Hs = 0.077m (a) WG11 (m) QALE-FEM exp time(s) (b) WG16 (m) QALE-FEM exp (m) time(s) QALE-FEM exp (c) WG time(s) Wave elevations recorded at various locations near the fixed FPSO (significant wave height 0.077m) Results of QALE-FEM agree well with the experimental data 10/11/2016 FROTH Workshop 18 November

27 Extreme Waves With Fixed FPSO Models Reliability of OpenFOAM How reliable are fully nonlinear predictions on wave elevations near fixed FPSO? OpenFOAM(UoB): Model 3, Hs = 0.077m Wave elevations recorded at various locations near the fixed FPSO (significant wave height 0.077m) Results of OpenFOAM agree well with the experimental data More Results on other cases 10/11/2016 FROTH Workshop 18 November

28 FNPT model (QALE-FEM): Model 3, Hs = 0.077m Extreme Waves With Fixed FPSO Models Reliability of QALE-FEM at City How reliable are fully nonlinear predictions on wave impacts on fixed FPSO? pressure (kpa) Pressure P3 experimental QALE-FEM time - t f (s) pressure (kpa) Pressure P6 experimental QALE-FEM time - t f (s) Comparison of pressure time histories at different locations (2 nd order piston wavemaker; significant wave height 0.077m) 10/11/2016 FROTH Workshop 18 November

29 Extreme Waves With Fixed FPSO Models Reliability of OpenFOAM How reliable are fully nonlinear predictions on wave impacts on fixed FPSO? OpenFOAM(UoB): Model 3, Hs = 0.077m Comparison of pressure time histories at different locations using OpenFOAM(significant wave height 0.077m) More Results 10/11/2016 FROTH Workshop 18 November

30 Extreme Waves With Fixed FPSO Models Reliability of OpenFOAM How reliable are fully nonlinear predictions on wave impacts on fixed FPSO? OpenFOAM(PU): Model 3, Hs = 0.077m pressure time histories using penfoam Without wave breaking, the viscous effects are insignificant and the FNPT is sufficient for evaluating wave run-up and impact. 10/11/2016 FROTH Workshop 18 November

31 Extreme Waves With Freely Floating FPSO Reliability of QALE-FEM at City How reliable are fully nonlinear predictions on motion responses of FPSOs? Using QALE-FEM QALE-FEM Experimental 10 5 QALE-FEM Experimental heave(m) pitch(deg) time(s) time(s) Comparison of motion time histories of the moored FPSO subjected to unidirectional waves (significant wave height 0.103m) Once again, the comparison indicates that the FNPT based QALE-FEM can produce satisfactory results in predicting motion response of floating bodies without breaking waves 10/11/2016 FROTH Workshop 18 November

32 How to efficiently model the wave impact and motion response of floating bodies in extreme sea? Linear theory & approach, Stokes or other nonlinear wave theories is not sufficient for extreme seas; Fully nonlinear potential theory ignoring viscos effects; CFD packages based on viscous model take too long Breaking, impact, viscosity, aeration, structure dynamics 10/11/2016 FROTH Workshop 18 November

33 How to efficiently model the wave impact and motion response of floating bodies in extreme sea? FNPT model solved by using QALE-FEM is efficient for large-domain and long-duration simulation ESBI: More Robust FNPT approach Spatial-temporal focusing random-sea simulation Can we have alternative and more efficient approach to solve the FNPT model? 10/11/2016 FROTH Workshop 18 November

34 ESBI: More Robust FNPT approach Further development on the FNPT model: ESBI Velocity on free surface Convolution Solved by FFT Liaising problem with FFT/IFFT Integration Solved by Boundary Integral Weakly singular De-singularity to perform the Cauchy integral in BI Anti-aliasing to make aliasing free for higher order convolution part Critical surface slope : a threshold of necessity of the integration part Wang, J., Ma, Q. W. (2015). Numerical techniques on improving computational efficiency of spectral boundary integral method. International Journal for Numerical Methods in Engineering, 102(10), /11/2016 FROTH Workshop 18 November

35 ESBI: More Robust FNPT approach Further development on the FNPT model: ESBI Time histories Wave Spectra The same accuracy as the QALE-FEM for the cases without wave breaking Much (>2 times) faster than the QALE-FEM Comparisons between the numerical results and experimental data recorded at m from the wave paddle(d = 2.93m, JONSWAP spectrum, H s = 0.103, peak period of 1.456s) 10/11/2016 FROTH Workshop 18 November

36 ESBI: More Robust FNPT approach Further development on the FNPT model: ESBI 3D simulations of Rogue waves embedded in random sea Quadruplets Domain: 32 x 32 peak wave lengths Duration: 100 peak periods CPU: Intel(R) Xeon(R) E5620@2.4GHz (8 cores) Total elapsed time: ESBI 5.7 hours Can effectively model 3D multiple wave groups in large domain with long duration 10/11/2016 FROTH Workshop 18 November

37 FROTH solution: to couple the FNPT model with NS model How to efficiently model the wave impact and motion response of floating bodies in extreme sea? Incident waves OpenFOAM domain Disturbance due to F.B. shall not be reflected from this B.C Disturbance to incident waves No reflection undesired from this BC Can we effectively remove the disturbance wave due to the floating bodies? 10/11/2016 FROTH Workshop 18 November

38 How to absorb the reflective wave in the open boundary and on the wavemaker? Self-adaptive wave absorber Using the wavemaker motion to absorb undesirable waves Novel development by considering local wave steepness; Overcome typical slow-drift associated with linear selfadaptive wavemaker; Considerably improve the absorbing efficiency, especially for low-frequency wave components Details of Self-adaptive wavemaker 10/11/2016 FROTH Workshop 18 November

39 How to absorb the reflective wave in the open boundary and on the wavemaker? Self-adaptive wave absorber The improved self-adaptive wave absorber is effective for wave group simulation without the need of input the spectrum for the wave absorber Using the self-correction and self-adaptive wavemaker, the requirement of the computational domain is significantly reduced Self-correction wavemaker Relative difference: ~0.1% Self-adaptive absorber 10/11/2016 FROTH Workshop 18 November

40 How to couple FNPT with OpenFOAM? Coupling QALE-FEM with OpenFOAM C++ Class Dynamic linked library(dll) Shared library(so) Damping zone to remove the reflected waves QALE-FEM class provides the inlet boundary condition, as well as the related parameters at the damping zone of OpenFOAM A efficient interpolation scheme M-SFDI has been developed in the QALE-FEM to estimate the velocity and pressure Xu GC, Yan S, Ma QW, 2015, Modified SFDI for fully nonlinear wave simulation, SEMS, Vol. 106, /11/2016 FROTH Workshop 18 November

41 Effectiveness of the coupled scheme Model test at Franzius-Institute, Leibniz Universitat Hannover Coupling QALE-FEM with OpenFOAM Wave tank: 110 m long, 2.2m wide and 2m deep. 0.7m mean water depth; Wave generator: piston wave paddle based on 2 nd order wavemaker theory; Cylinder: 0.22m diameter; Wave gauges and pressure sensors 10/11/2016 FROTH Workshop 18 November

42 Coupling QALE-FEM with OpenFOAM Effectiveness of the coupled scheme-fixed cylinder OpenFOAM domain: length 6D centred at the cylinder cylinder surface facing incident wave (f l = 0.34 Hz to f u = 1.02 Hz. G a = 0.003), QALE-FEM OpenFOAM only QALE-FEM with OpenFOAM CPU time Desktop PC 4 cores ~4 hours Newmann cluster 192 cores ~1 week(mmu) Intel(R) Xeon(R) E5620@2.4GHz (8 cores): ~10 hours 10/11/2016 FROTH Workshop 18 November

43 Coupling QALE-FEM with OpenFOAM Effectiveness of the coupled scheme-fixed cylinder (a)x=24.43m Exp QALE-FEM QALE/OpenFOAM / max time/t / max Exp QALE-FEM OpenFOAM (b)x=25.00m time/t Wave elevation recorded at two wave gauges in front of the cylinder Good agreement between the numerical results by QALE-FEM and the hybrid model with the experiment 10/11/2016 FROTH Workshop 18 November

44 Coupling QALE-FEM with OpenFOAM Effectiveness of the coupled scheme-fixed cylinder (a)z=0.6 max p / c Exp QALE-FEM OpenFOAM p / c 2 (b)z= max Exp time/t QALE-FEM OpenFOAM time/t Normalised pressure at different location on the cylinder surface Similar agreement between numerical results and experimental results are found in pressure data

45 Coupling QALE-FEM with OpenFOAM Effectiveness of the coupled scheme-fixed cylinder (c)z=-0.77 max p / c Exp QALE-FEM OpenFOAM (d)z=-1.46 time/t max p / c Exp QALE-FEM OpenFOAM time/t Normalised pressure at different location on the cylinder surface The QALE-FEM/OpenFOAM results agree well with the experimental data

46 Coupling QALE-FEM with OpenFOAM Effectiveness of the coupled scheme moving cylinder Unidirectional focusing waves: 32 components; Frequency range: 0.34 Hz to 1.02 Hz with different wave height. Cylinder Moving towards the wave paddle with speed ranging from 0.25 to 0.75m/s Ensure the cylinder reaches the focusing point at focusing time 10/11/2016 FROTH Workshop 18 November

47 Effectiveness of the coupled scheme moving cylinder Challenges of numerical modelling Coupling QALE-FEM with OpenFOAM Approach 1: introduce an opposite uniform current representing forwarding structures(commonly used) Interaction between the wave and current may significantly influence the waves, affecting the formation of the focusing waves; Approach 2: directly model the motion of the structures Needs frequent remeshing or significantly reduce the mesh quality and suffer from mesh distortion for moving-mesh scheme 10/11/2016 FROTH Workshop 18 November

48 Effectiveness of the coupled scheme moving cylinder A wave tank: QALE- FEM to model the wave without cylinder; A small domain near the cylinder Moving at the speed of the cylinder Boundary condition obtained by the full-domain simulation above A translational zone to damp the disturbed waves by the cylinder QALE-FEM or OpenFOAM Coupling QALE-FEM with OpenFOAM Rectangle tank: Initial and BC by 2 nd order, Ws =0.5, Hs=5m, gamma =3.3 PM spectrum ; small domain: QALE-FEM for demonstration 10/11/2016 FROTH Workshop 18 November

49 Coupling QALE-FEM with OpenFOAM Effectiveness of the coupled scheme moving cylinder cylinder surface facing incident wave (f l = 0.34 Hz to f u = 1.02 Hz. G a = 0.002, cylinder moves towards the wave paddle with speed of 0.25m/s (small domain: OpenFOAM) 10/11/2016 FROTH Workshop 18 November

50 Coupling QALE-FEM with OpenFOAM Effectiveness of the coupled scheme moving cylinder Exp QALE-FEM/OpenFOAM 30 pressure(100pa) time(s) Time history of pressure at different locations on the cylinder surface facing incident wave (f l = 0.34 Hz to f u = 1.02 Hz. G a = 0.002, cylinder moves towards the wave paddle( 0.25m/s) Acceptable agreement between the hybrid modelling results and the experimental data of the pressure recorded on the cylinder surface 10/11/2016 FROTH Workshop 18 November

51 Summary of achievements How to identify the significance of the nonlinearity associated with floating bodies in extreme sea? How reliable are numerical results obtained by using existing nonlinear models? How to efficiently model the wave impact and motion response of floating bodies in extreme sea? Physical model testing reveal importance of 4-th order harmonics Explore the significance of nonlinearity associated with FPSOs in extreme sea Develop self-correction and selfadaptive wavemaker for wave generation and absorption; Investigate the reliability of FNPT model and OpenFOAM on wave impacts and motion responses of FPSO Develop ESBI based on FNPT which effectively models non-breaking 3D extreme waves in large domain for long duration; A hybrid model combining QALE-FEM with OpenFOAM has been developed; The hybrid model considers the viscous/turbulent effects & dramatically improve the computational efficiency 10/11/2016 FROTH Workshop 18 November

52 Thank You WP3 (City) Qingwei Ma & Shiqiang Yan School of Mathematics, Computer Science & Engineering, City University London WP1(PU) Tri Mai, Deborah Greaves & Alison Raby School of Marine Science and Engineering Plymouth University WP5(UoB) Feng Gao & Jun Zang Department of Architecture and Civil Engineering, University of Bath

53 Numerical Modelling at City Numerical modelling at City ESBI QALE-FEM MLPG-R Immersed Boundary FNPT models Viscous models OpenFOAM P1 (Bar) Experimental data (P1) interfoam compressibleinterfoam compressiblemutiphaseinterfoam (a) Time (s) x 10-3 F2 (kn) Experimental data (F2) interfoam compressibleinterfoam compressiblemutiphaseinterfoam Time (s) x 10-3 Comparison of pressure and force with model tests (c) 10/11/2016 FROTH Workshop 18 November

54 (m) (m) How to reliably model the highly nonlinear multiple wave systems? 0 Gauge date used for the correction experimental QALE-FEM piston:1st time(s) 0.05 Obtain predicted spectrum using FFT; Compare with the measured spectrum; Correct experimental QALE-FEM piston:3rd time(s) (m) Extreme Waves without structures Numerical Modelling at City: Self-Correction Wavemaker experimental QALE-FEM piston:2nd time(s) The wave elevations obtained at different iterative steps during self-correction based on the gauge data at WG1(12.391m from the wave paddle, significant wave height 0.103m). 10/11/2016 FROTH Workshop 18 November Obtain predicted spectrum using FFT at one point; Compare with the measured spectrum; Correct Usually three iterations are sufficient for non-breaking focusing waves

55 Extreme Waves With Fixed FPSO Models Reliability of OpenFOAM How to reliably model the highly nonlinear multiple wave systems? Wave elevations near fixed FPSO OpenFOAM(UoB): Model 2, Hs = 0.077m Wave elevations recorded at various locations near the fixed FPSO (significant wave height 0.077m) 10/11/2016 FROTH Workshop 18 November

56 Extreme Waves With Fixed FPSO Models Reliability of OpenFOAM How to reliably model the highly nonlinear multiple wave systems? Wave elevations near fixed FPSO OpenFOAM(UoB): Model 1, Hs = 0.077m Wave elevations recorded at various locations near the fixed FPSO (significant wave height 0.077m) Similar agreement is observed at the OpenFOAM modelling at UoB 10/11/2016 FROTH Workshop 18 November

57 Extreme Waves With Fixed FPSO Models Reliability of OpenFOAM How reliable fully nonlinear predictions on wave impacts on fixed FPSO are? OpenFOAM(UoB): Model 2, Hs = 0.077m Comparison of pressure time histories at different locations using OpenFOAM(significant wave height 0.077m) 10/11/2016 FROTH Workshop 18 November

58 Extreme Waves With Fixed FPSO Models Reliability of OpenFOAM How reliable fully nonlinear predictions on wave impacts on fixed FPSO are? OpenFOAM(UoB): Model 1, Hs = 0.077m Comparison of pressure time histories at different locations using OpenFOAM(significant wave height 0.077m) 10/11/2016 FROTH Workshop 18 November

59 Efficiency FROTH: Fundamentals and Reliability How to absorb the reflective wave in the open boundary and on the wavemaker? Problems with the existing technologies Self-adaptive wave absorber ka= ka= ka= ka= Frequency Efficiency becomes lower as the increase of the wave steepness Not effective for waves with lower and higher frequencies Efficiency = 1 Comparing the results with longer tank simulation May suffer from instability problem 10/11/2016 FROTH Workshop 18 November

60 How to absorb the reflective wave in the open boundary and on the wavemaker? Problems with the existing technologies Slow drift Self-adaptive wave absorber (1) Shift due to absorb long wave front after the wave reaches the absorber (2) Constant 2 nd order difference term (subharmonics) existing in the wave elevation, leading to a constant velocity component 10/11/2016 FROTH Workshop 18 November

61 How to absorb the reflective wave in the open boundary and on the wavemaker? Improvement of the current technology Self-adaptive wave absorber automatically omit the 2nd order difference term no longer suffering from low drift ka = 0.15, fre = 0.6 Absorbing efficiency is improved for low-frequency and high-frequency 10/11/2016 FROTH Workshop 18 November