A model of the flow around bilge keels of FPSO hull sections subject to roll motions

1. A model of the flow around bilge keels of FPSO hull sections subject to roll motions The University of Texas at Austin Ocean Engineering Group S. A. Kinnas, Y.-H. Yu, B. Kacham, and H. S. Lee Supported by the Offshore Technology Research Center (OTRC)

2. Introduction • Motivation - FPSO hulls have often been subject to amplitudes of roll motion which seem to be larger than the predicted using potential flow solvers.

3. Introduction • Objectives - Develop efficient computational model to predict the hydrodynamic coefficients of FPSO hulls in roll motions. - Investigate effectiveness of bilge keels on roll mitigation

4. Numerical Formulation • 2D Continuity and Momentum Equations • Conservation form v q y u x

5. Ni’s Lax Wendroff method for time B C • Artificial Viscosity A D Node 1 • SIMPLE method for Pressure Correction to satisfy the continuity equation:

6. Oscillating Flow past a Flat Plate • Fluid domain and Boundary Conditions

7. Definition of Keulegan-Carpenter Number • Horizontal force on Plate (Morison’s equation)

8. Background - Sarpkaya & O’Keefe’s Experiment (1995)

9. Comparison of results from Euler and Navier-Stokes solvers, and Sarpkaya’s measurements Inertia Coefficients (Cm) Drag Coefficients (Cd)

10. Vorticity & Streamlines at t=0xT (KC=1) • Vorticity & Streamlines at t=T/4 (KC=1) Navier-Stokes Solver Euler Solver

11. Vorticity & Streamlines at t=T/2 (KC=1) • Vorticity & Streamlines at t=3T/4 (KC=1) Euler Solver Navier-Stokes Solver

12. Movie (KC=1)

13. Movie (KC=10)

14. Comparison of force over one period (KC=1)

15. FPSO Hull Section Motion • Fluid domain and Boundary Conditions

16. Boundary Condition on Free-surface • Body motion (Roll motion) • Added mass and damping coefficients 2b

17. Grid and geometry details

18. Comparison of Added mass and Damping coefficients for Heave motion (B/D=2, No bilge Keel)

19. Vorticity contour and Streamlines for roll motion (6% bilge keel, roll angle=0.05(rad), and Fn = 0.8) t = 0xT t = T/4 t = T/2 t = 3T/4

20. Comparison of added mass and damping coefficients for various sizes of bilge keel Added mass Coefficients Damping Coefficients

21. Conclusions • Developed CFD model to solve the Euler equations around a flat plate, and an FPSO hull section subject to roll motions. • Validated the present method : - Flat plate subject to an oscillating flow: Euler results comparable to those from Navier-Stokes and experimental data - Hull in Heave motion: Present method predicted hydrodynamic coefficients well. - Hull in Roll motion: * Euler solver is capable of capturing the separated flow from bilge keels. * Present solver can predict expected increase in added mass, and damping coefficients with increasing bilge keel size.

22. Future Work • Implement viscous flow terms in the case of FPSO hulls with and without bilge keels • Use the modified hydrodynamic coefficients at each FPSO hull section, to correct the results from potential flow solvers. • Validate the method with existing and future experiments on FPSO hulls to be carried out at OTRC’s Wave Basin.