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FPSO Roll Mitigation

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  1. FPSO Roll Mitigation PI: Prof. Spyros A. Kinnas Current Research Staff: Yi-Hsiang Yu, Vimal Vinayan, Dr. Hanseong Lee Former Research Staff: Karan Kakar (MS 2002), Bahrani Kacham (MS 2004) The University of Texas at Austin Ocean Engineering Group MMS/OTRC Review Meeting - UT Austin

  2. Motivation:FPSO hulls have been reported to be subject to excessive roll motions, which may lead to fatigue of mooring lines, disruption of operation, and discomfort of the crew MMS/OTRC Review Meeting - UT Austin

  3. Objective:Develop robust, validated computational model to study effect of bilge keel shape on roll motions MMS/OTRC Review Meeting - UT Austin

  4. Related Publications • Kinnas, S.A., Yu, Y.-H., Vinayan, V., Kacham, K., Modeling of the Unsteady Separated Flow over Bilge Keels of FPSO Hulls under Heave and Roll Motions, The 15th International Offshore and Polar Engineering Conference, 2005, (Abstract accepted , Paper under preparation). • Kinnas, S.A., Vinayan, V., Yu, Y.-H., Modeling of the Viscous Flow Around FPSO Hull Sections under Heave and Roll Motions, OMAE 2005, (Abstract accepted , Paper under preparation). • Kacham, B., Inviscid and Viscous 2D Unsteady Flow Solvers Applied to FPSO Hull Roll Motions, MS thesis, UT Austin, Ocean Engineering Group, Department of Civil Engineering, December 2004 (also UT-OE Report 04-7) . • Kinnas, S.A., Yu, Y.-H., Lee, H., Kakar, K., Modeling of Oscillating Flow Past a Vertical Plate, The 13th International Offshore and Polar Engineering Conference, Honolulu, Hawaii, May 25-30, 2003, pp.218-226. • Kinnas, S.A., Yu, Y.-H., Kacham, B., Lee, H., A Model of the Flow around Bilge Keels of FPSO Hull Sections subject to Roll Motions, The 12th Offshore Symposium, Texas Section of SNAME, Houston, TX, February 19, 2003. • Kakar, K., Computational Modeling of FPSO Hull Roll Motions and Two-component Marine Propulsion Systems , MS thesis, UT Austin, Ocean Engineering Group, Department of Civil Engineering, August 2002 (also UT-OE Report 02-3) . MMS/OTRC Review Meeting - UT Austin

  5. Today’s Presentation Part I: Modeling of the Unsteady Separated Flow over Bilge Keels of FPSO Hulls under Heave and Roll Motions~ Finite VolumeMethod (Viscous Flow) Part II: Application of Panel Method to 2-D FPSO Hulls Subject to Roll Motion (Inviscid Flow) Copies of movies/papers and today’s presentations may be downloaded from http://cavity.ce.utexas.edu/kinnas/fpso MMS/OTRC Review Meeting - UT Austin

  6. Part I:Modeling of the Unsteady Separated Flow over Bilge Keels of FPSO Hulls under Heave and Roll Motions Yi-Hsiang Yu (Ph.D. Student) MMS/OTRC Review Meeting - UT Austin

  7. Overview of the Presentation • Numerical Formulation • Governing Equations • Numerical Method • Effect of Moving Grid • Results • Oscillating Flow Past a Vertical Plate • Submerged Body Subject to Heave or Roll motions, and the effect of Reynolds No. • FPSO Hull Subject to Roll Motions • Effect of Length & Orientation Angle of Bilge Keels • Conclusions and Future Work MMS/OTRC Review Meeting - UT Austin

  8. Numerical Formulation • Governing Equation Non-Dimensional Governing Equation (Navier-Stokes Equation & Continuity Equation) where U represents the velocity; Q is the force term; R indicates the viscous term; and the Reynolds number is define as Re = Umh/ν; and the length scale, h, is a representative length in the problem being solved. • Based on Finite Volume Method for Euler equations, Choi (PhD 2000), Choi and Kinnas (JSR, 2003) • Cell Based Finite Volume Method Collocated variable, non-staggered grid arrangement, Non-orthogonal grids MMS/OTRC Review Meeting - UT Austin

  9. Crank-Nicolson Method for Time Marching where f represents the summation of the convective terms, the viscous terms and the pressure terms at the present time step n and the next time step n+1. • Pressure-correction Method • SIMPLE method (Patankar 1980) where p’ is the pressure correction, V’faceis the velocity correction term, әp’ /әnis the pressure correction derivative with respect to the normal direction of the cell face, V*face= (u*; v*) is the predicted velocity vector obtained from the momentum equation. MMS/OTRC Review Meeting - UT Austin

  10. Moving Grid When the grid is moving, additional terms need to be taken into account. where (ugrid, vgrid) is the velocity of the moving grid; and represents the total change in the value of u with both increment in time and the corresponding change in the location of the point. When the above equation is substituted into the momentum equation MMS/OTRC Review Meeting - UT Austin

  11. Results • The main focus of this research is to model the unsteady separated viscous flow over the bilge keels of a FPSO hull subject to roll motions and to determine its effect on the hull forces. • Development and applications of the NS2D solver • Oscillating flow over a vertical plate. • Submerged body with or without bilge keels. • FPSO hull subject to heave and roll motions. (The effects of the bilge keels and the free surface are taken into account). MMS/OTRC Review Meeting - UT Austin

  12. Oscillating Flow Past a 2-D Vertical Plate Previous Results MMS/OTRC Review Meeting - UT Austin

  13. Drag & Inertia Coefficient for a Range of • Kc=UmT/h (0.5 < Kc < 5) MMS/OTRC Review Meeting - UT Austin

  14. FVM (Inviscid) Potential Solver S • Validation of finite volume method (FVM) w/o viscosity with those of panel method (see Part II) for a submerged hull subject to roll motions (Kacham, MS 2004) The pressure distribution along the submerged hull without bilge keels  MMS/OTRC Review Meeting - UT Austin

  15. t/T=0.25 t/T=0.50 Pressures on submerged hull with bilge keels Effect of Reynolds number MMS/OTRC Review Meeting - UT Austin

  16. FPSO Hull Subject to Roll Motions Grid used by Kakar,MS 2002, UT Austin B=2b Grid improved by Kacham,MS 2004, UT Austin MMS/OTRC Review Meeting - UT Austin

  17. Comparison of added mass coefficients from previous solver and other results Comparison of damping coefficients from previous solver and other results Kacham, MS 2004, UT Austin • Added Mass and Damping Coefficients of FPSO Hull without Bilge Keels -Without moving grid MMS/OTRC Review Meeting - UT Austin

  18. Comparison of added mass coefficients from the previous solver and other results Comparison of damping coefficients from the previous solver and other results • Added Mass and Damping Coefficients of FPSO Hull with 4% Bilge Keels – Without moving grid Kacham, MS 2004, UT Austin MMS/OTRC Review Meeting - UT Austin

  19. Preliminary Results of Current Work(FPSO Subject to Roll Motion) • Numerical Scheme Improvements • Crank-Nicolson Method for Time Marching. • Moving Grid. • Grid and Geometry Details • Convergence studies in space and in time. • Investigation of effects of bilge keel length and orientation angles. • Consider only the linear free surface effect. MMS/OTRC Review Meeting - UT Austin

  20. Bilge Keels width (length) • FPSO Hull Subject to Roll Motions θ=20° θ=45° θ=70° θ MMS/OTRC Review Meeting - UT Austin

  21. Convergence Study in Space and in Time Fn=1.0, 2% Bilge Keels MMS/OTRC Review Meeting - UT Austin

  22. Table of Added Mass and Damping Coefficient MMS/OTRC Review Meeting - UT Austin

  23. Comparison of added mass coefficients from the present solver and other results Comparison of damping coefficients from the present solver and other results • Added Mass and Damping Coefficients of FPSO Hull Subject to roll motions MMS/OTRC Review Meeting - UT Austin

  24. The wave profile, pressure distribution and vorticity contour plot of a FPSO hull with 4% bilge keels subject to the roll motion at Fn=0.6. MMS/OTRC Review Meeting - UT Austin

  25. The vorticity contour plot of a FPSO hull with 4% bilge keels subject to the roll motion at Fn=0.6. MMS/OTRC Review Meeting - UT Austin

  26. Comparison of added mass and damping coefficients between different angles of 4% bilge keels with Fn=1.0 • Added Mass and Damping Coefficients at Different Angles of Bilge Keels Similar trend to that in Na 2002 and Yeung 2003. MMS/OTRC Review Meeting - UT Austin

  27. The vorticity contour plot of FPSO hulls with 4% horizontal or vertical bilge keels subject to the Roll motion at Fn=1.0. MMS/OTRC Review Meeting - UT Austin

  28. Conclusions • A numerical scheme for solving the unsteady Navier-Stokes equations has been developed and validated with experiments and other numerical results. • The method was applied in the case of an FPSO hull undergoing roll motions. The effects of the bilge keels and of the free surface (linear) were also taken into account. • The effect of different angles of bilge keels has been studied The trend was found to be similar to the Na 2002 experiments and the Yeung 2003 numerical results (the geometry is not exactly the same though). MMS/OTRC Review Meeting - UT Austin

  29. Future Work • More convergence studies have to be performed, especially sensitivity studies in terms of grid, time step, and domain size for different Froude numbers. • Apply method for larger amplitudes of roll motion and compare with experiments and other numerical results. • Use the same geometry as that in the experiments in the case of vertical or horizontal bilge keels. • Consider the non-linear free surface effects (see Part II) • Extend the model in 3-D and compare with experiments and other numerical results. MMS/OTRC Review Meeting - UT Austin

  30. Part IIApplication of Panel Method to 2-D FPSO Hulls Subject to Roll Motion Vimal Vinayan (Ph.D. student) MMS/OTRC Review Meeting - UT Austin

  31. Mathematical Background • Navier-Stokes Equations • Potential Flow (Inviscid / Irrotational) • Green’s Second Identity on simplification, MMS/OTRC Review Meeting - UT Austin

  32. Mathematical Background Contd.. MMS/OTRC Review Meeting - UT Austin

  33. Mathematical Background Contd.. • Boundary Condition : F(surface assumed to be a material surface) • Kinematic Boundary Condition Nonlinear/Exact Linear • Dynamic Boundary Condition Nonlinear/Exact Linear • Time dependent boundary conditions MMS/OTRC Review Meeting - UT Austin

  34. Mathematical Background Contd.. • Boundary Condition : H • Kinematic Boundary Condition MMS/OTRC Review Meeting - UT Austin

  35. Mathematical Background Contd.. • Boundary Condition : Σ • Kinematic Boundary Condition (No flux) Computation stopped before the radiating waves reach the outer boundary to avoid reflection • Boundary Condition : B • Kinematic Boundary Condition (No flux) MMS/OTRC Review Meeting - UT Austin

  36. Forces and Moments • Pressure (Hull) Dynamic Pressure Hydrodynamic Coefficients MMS/OTRC Review Meeting - UT Austin

  37. Numerical Formulation Contd.. • Time Stepping – Modeling of Free Surface Mixed Eulerian – Lagrangian (MEL) Method of Longuet-Higgins and Cokelet (1976) • Euler Explicit • Fourth-Order Runge - Kutta • Fourth-Order Adams-Bashforth • Young and Kinnas 2002, Young (PhD), 2002 (A BEM Technique for the Modeling of Supercavitating and Surface-Piercing Propeller Flows, 24th Symposium on Naval Hydrodynamics, Fukuoka, Japan) MMS/OTRC Review Meeting - UT Austin

  38. Results – Roll (5o Roll) • Moment history • Roll amplitude of 5 degrees • Comparison of results for Linear and Nonlinear algorithms MMS/OTRC Review Meeting - UT Austin

  39. Results – Roll (20o Roll) • Moment history • Roll amplitude of 20 degrees • Comparison of results for Linear and Nonlinear algorithms MMS/OTRC Review Meeting - UT Austin

  40. Results – Roll (5o Roll) • Pressure Distribution • Roll amplitude of 5 degrees • Comparison of results for Linear and Nonlinear algorithms MMS/OTRC Review Meeting - UT Austin

  41. Results – Roll (5o Roll) MMS/OTRC Review Meeting - UT Austin

  42. Results – Roll (20o Roll) • Pressure Distribution • Roll amplitude of 20 degrees • Comparison of results for Linear and Nonlinear algorithms MMS/OTRC Review Meeting - UT Austin

  43. Results – Roll (20o Roll) MMS/OTRC Review Meeting - UT Austin

  44. Results - Roll Wave Elevation (50 Roll) MMS/OTRC Review Meeting - UT Austin

  45. Results - Roll Wave Elevation (50 Roll) NOTE: Non-linear wave profiles are NOT (stbd/port) anti-symmetric MMS/OTRC Review Meeting - UT Austin

  46. Results - Roll Wave Elevation (200 Roll) MMS/OTRC Review Meeting - UT Austin

  47. Results - Roll Wave Elevation (200 Roll) NOTE: Non-linear wave profiles are NOT (stbd/port) anti-symmetric MMS/OTRC Review Meeting - UT Austin

  48. Non-linear Results – Roll Hull Motion and Wave Elevation (200 Roll) MMS/OTRC Review Meeting - UT Austin

  49. Non-linear Results - Roll Hull Motion and Wave Elevation (200 Roll) NOT to scale! MMS/OTRC Review Meeting - UT Austin

  50. Conclusions • Linear and Nonlinear algorithms developed and the results were compared for different amplitudes of roll. • Effect of Nonlinearity important for higher degrees of roll. Future Work • Improve Nonlinear algorithm to investigate high degrees of roll motion. • Quantify effects of nonlinearity on hydrodynamic coefficients. • Extend current free-surface tracking method in the case of the Navier Stokes Solver • Apply method in a strip-wise sense to predict 3-D FPSO hull coefficients and compare with experiments MMS/OTRC Review Meeting - UT Austin