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

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). Introduction. Motivation

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

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  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.

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