Simulation of Offshore Structures in Virtual Ocean Basin (VOB)

Transcription

1 Simulation of Offshore Structures in Virtual Ocean Basin (VOB) Dr. Wei Bai 29/06/2015 Department of Civil & Environmental Engineering National University of Singapore

2 Outline Methodology Generation of nonlinear waves Wave diffraction by an array of cylinders Wave interaction with side-by-side barges Payload in vicinity of barge 2

3 Methodology Generation of nonlinear waves Wave diffraction by an array of cylinders Wave interaction with side-by-side barges Payload in vicinity of barge 3

4 Numerical Model Model sketch Wavemaker Z SF O' Z' O X' X Damping Swm SB1 SB2 Sw SD Sketch of Numerical Wave Tank 4

5 Mathematical Formulation Fully nonlinear potential flow (FNPF) Laplace eqn. BCs Original model on free surface: (Lagrangian) 2 0 DX Dt D 1 2 gz Dt 2 Separation X X X I I S S 2 S Decomposition model 0 DX S I Dt DS 1 1 gzs Dt I on body surface: n V n S n V n I n Incident flow I,, evaluated explicitly I X I 5

6 Methodology Generation of nonlinear waves Wave diffraction by an array of cylinders Wave interaction with side-by-side barges Payload in vicinity of barge 6

7 Wave Generation System Comparison of transfer function with Bi esel s equation 7

8 Focused waves in 2D NWT (designed spectra) An example of 2D focal event under designed spectrum (Case B55) Validation on normalized power spectra of Cases B (deep water, broad band), compare with Baldock and Swan,

9 Multi-directional waves in 3D NWB Wavemaker configuration in 3D numerical wave basin 9

10 Multi-directional waves in 3D NWB Evolution of irregular waves 10

11 Methodology Generation of nonlinear waves Wave diffraction by an array of cylinders Wave interaction with side-by-side barges Payload in vicinity of barge 11

12 Validation Comparison with experiments 1 for 0 heading y Cylinder 1 Cylinder Experiment Present x Cylinder 3 Cylinder Experiment Present Linear x(m) Maximum elevation mean k x(m) Mean elevation Radius a=0.203m space l=4a depth d=5a Amplitude A=0.049m Frequency ω=5.024rad/s 1. Ohl et al. (2001) 12

13 Case study Four cylinders in square 45 heading Radius a=0.2 space l=4a depth d=5a Amplitude A=0.02 frequency ka=

14 Near-trapping Mode shape bird view Elevation η/a Linear solution predicts the resonant frequency ka = 1.66 Near standing wave within the array Radius a=0.2 space l=4a depth d=5a ka=1.57 frequency ka=

15 Near-trapping High wave elevation at near-trapped mode Cylinder 2 y Wave amplitude along x-axis BC ka 1.66 ka0.754 ka0.468 Cylinder 1 Cylinder 3 A B C D Cylinder 4 x Near-trapping frequency x 15

16 Methodology Generation of nonlinear waves Wave diffraction by an array of cylinders Wave interaction with side-by-side barges Payload in vicinity of barge 16

17 Side-by-side barges Numerical model Same barges in Molin et al. (2009) L = 2.47m B = 0.6 m Gap width = 0.12m Draft = 0.18m 17

18 Side-by-side barges Comparisons 7 Free surface RAOs Present (low steepness) Linear Experiments Gap surface amplitudes at midship Comparisons with experiments by Molin et al (2009) and linear program Frequency rad/s 18

19 Side-by-side barges Resonant modes Mode 1: ω = 5.75 rad/s Mode 3: ω = 6.85 rad/s (a) (b) /A x Wave envelope along gap 19

20 Side-by-side barges Random wave input Unidirectional Input Able to achieve multi-directional Gap surface RAOs at midship Present Molin experiments Frequency rad/s 20

21 Freely floating barges An example Length 2m Width 1m Distance 1m Draft 0.3m Center of gravity: half draft 21

22 Freely floating barges Time histories of motions for free barges Surge Roll On the barge in head wave at ω =6.0 rad/s Sway Heave Pitch Yaw No restoring force/moment in Surge, Sway and Yaw Apparently there is drift 22

23 Freely floating barges Comparison of first order motion with HydroStar First order motion on the barge in head wave 23

24 Barges with interconnections 0.5 Side-by-side interconnected barges 2.0 Barge Barge 2 Rigid Middle hinge End hinges 24

25 Barges with interconnections Hydrodynamic force and motion equations If bodies are interconnected, motion equations become M C D K A Q T T D2 M2 C2 K 2 A2 Q2 K1 K 2 0 Fcst 0 where K1, K2 are constraints matrix due to interconnection Fcst is interconnection force 25

26 Barges with interconnections Rigid connection Surge Roll On Barge 1 in head wave at ω =6.0 rad/s Sway Heave Pitch Yaw Surge, Heave, Pitch not affected. Sway, Roll, Yaw near zero due to rigid connection. 26

27 Barges with interconnections Middle hinge connection Only Yaw drift much reduced, other DOF not much changed End hinges connection Yaw drift slightly increased 27

28 Methodology Generation of nonlinear waves Wave diffraction by an array of cylinders Wave interaction with side-by-side barges Payload in vicinity of barge 28

29 Payload close to a barge Computational mesh for different scenarios Wave propagating form left to right (b) (a) (c) (a) Submerged cylinder with barge in head sea (b) Upstream submerged cylinder with barge in beam sea (c) Downstream submerged cylinder with barge in beam sea 29

30 Payload close to a barge 3D trajectory of cylinder motion Trajectory x XZ projection Trajectory x XZ projection Vertical displacement Vertical displacement t/t Horizontal displacement t/t 40 Horizontal displacement Single submerged cylinder in domain Cylinder with barge in head sea No downward motion: cable length = 0.8d, a = 0.02, ω = 2.0, cylinder 0.2 d below the free surface (d = tank depth) 30

31 Low frequency pendulum motion cbl (sin 5 ) / a Cyl only Head sea t/t mean cbl (sin 5 ) / a -4 Beam sea Up Beam sea Dn t/t ω 2ω cable length of 0.8d, a = 0.15, ω =2.0 ωlow Appears as a harmonics of 1/10 ω 31

32 Payload with downward velocity 15 mod = mod = 0.01 mod = Cyl only Head sea M y / r 3 a t /T 4 2 mod = mod = 0.01 mod = 0.02 draft T / r 2 a t /T x /a Real time cylinder positioning under water for cylinder only and head sea scenarios: cbl = 0.8d, ω = 2.0, a = 0.015, mod =

33 Nonlinear dynamics of payload Frequency doubling phenomenon exists between ω of 1.5 to 2.0. Possible chaotic behavior for ω near 2.0 and above Payload pendulum motion for different motion frequencies at a = 0.01 and L c = 0.5d [Beam Sea Up]: row 1: time history of motion; row 2: phase trajectories; and row 3: Poincarémap Complex overlapping in the phase plane with increasing ω, indicating increase of nonlinearity 33

34 Thank you!