Summary
Objective
Field observations indicate that FPSO’s roll more than expected based on their design and model tests. This can potentially lead to riser fatigue and operations difficulties (degraded process performance, operational limits on material transfer, crew comfort and effectiveness). The objective of this project is to develop sufficient knowledge to understand roll in realistic ocean environments and use that knowledge to mitigate excessive roll through suppression devices or design.
Approach
Develop and validate a theoretical model to describe FPSO roll motions in realistic metocean environments. This model will then be used to study performance and effectiveness of roll suppression devices and methodologies. Finally, the predicted performance of roll suppression device(s) using the present model will be validated versus model test data and field observations. Data for developing and validating the present roll predictive model, and for studying the behavior of roll suppression devices are being obtained from a separate but related project (FPSO Responses in Gulf of Mexico Environments). Some data exist, and additional data will be obtained during experiments this year. Data are also available from recent 2-D roll study in a flume at Texas A&M (Chang).
Deployment of Results
The result of this project will be a validated analytical model to predict the roll of FPSO’s and the effectiveness of roll suppression devices. This model will be available to sponsors to use in assessing roll and the need for suppression for specific FPSO designs. Roll data from experiments and from numerical predictions of roll and the performance of roll suppression devices will also be available to sponsors for their use in developing realistic roll criteria to evaluate FPSO designs in roll, and roll suppression devices.
Project Plan
Scope of Work:
In year one of this 3-year project modeling of a 2-D hull section subject to prescribed roll motions was started. Preliminary studies have indicated that a finite volume method (developed in the past to predict the flow around propulsors or thrusters) that solves for the unsteady flow in the time domain is the most computationally efficient, yet accurate method, in dealing with the separated flow behind the bilge keels of a hull. In addition, modeling of the motions of an actual FPSO hull (provided by Dr. Ward) subject to a given unidirectional wave using WAMIT (which is available to OTRC through its participation in Professor J.N. Newman’s JIP) was started.
In the second year of this project an unsteady finite volume method that solves for the Euler equations around a 2–D hull section (with and without bilge keels) subject to roll motions was developed. The method was applied first in the case of an oscillating flat plate. In this case a laminar flow Navier-Stokes solver in which the non-slip conditions were applied on the plate was also developed. The resulting unsteady force from the Euler and the Navier-Stokes solvers seemed to be in very good agreement, thus justifying the use of the (faster) Euler solver in the case of the hull with or without a bilge keel. The results seemed also to be in reasonable agreement with the measurements of Sarpkaya. The effects of the free-surface were accounted for by using the linearized kinematic and dynamic boundary conditions (which had to be recasted in terms of velocities instead of potential), while it was found that a radiation boundary condition was not necessary. The results in the case of a rectangular hull in heave were compared with those of Vugts and the agreement was found to be very good (in terms of added mass and damping coefficients) over a wide range of frequencies. The effect of the bilge keels were studied in the case of heave and roll motions and comparisons with other methods were carried out. In addition modeling of the motions of an actual FPSO hull (provided by Dr. Ward) subject to a given unidirectional wave using WAMIT (which is available to OTRC through its participation in Professor J.N. Newman’s JIP), and by rendering the resulting motions via a Java-3D applet (supported through another NSF through OTRC contract on the Electronic Classroom on Ocean Wave Theory) was completed.
In year three of this project we propose that we first extend our method in order to include the non-linear free-surface effects. These effects are expected to be important for roll angles higher than 10 degrees, especially since angles of 20 degrees or higher have been reported on FPSOs. The current method employs linearized free-surface conditions. In the proposed work we will couple our finite volume method with a free-surface tracking or capturing technique (such as volume of fluid or level set methods) by applying the non-linear dynamic and kinematic boundary conditions. It should be noted that the moving grid (developed in the previous year) will be more appropriate in this case. Once this method is completed it will allow us to capture the non-linear free surface effects in the case of larger roll angles. We are currently working on extending our panel method to allow for non-linear boundary conditions by tracking the location of the free surface in time (using the method of Young and Kinnas, 2002, originally developed for surface piercing hydrofoils). The non-linear panel method should be much less computer intensive than the finite volume method, and will allow us to compare the effects of viscosity on the hydrodynamic coefficients in the case of large roll motions. It will also provide us with an alternative numerical solution (pressure distribution and roll moment on the hull, as well as the characteristics of the radiated waves) against which we will compare the numerical accuracy of the finite volume method in the absence of viscosity.
The most recent method (without or with the non-linear free surface effects, depending on the amplitude of the roll angle) will be applied at various stations of an FPSO hull and will be integrated along its length in order to provide estimates of the 3-D hydrodynamic coefficients which will then be validated against available measurements (including those at OTRC/TAMU mentioned above). Studies will be performed in order to assess the effect of the bilge keel shape (extent and orientation, e.g. vertical, horizontal, or at an angle) on the added mass and damping coefficients at different Froude numbers (i.e. frequencies of oscillation). The results of this study (in terms of graphs of added mass and damping coefficients as a function of Froude number for various bilge keel extents and orientation angles) will provide guidance to be used at the initial stages of bilge keel design to mitigate roll motions.
Time permitting, we also plan on starting developing a 3-D version of our method, by essentially extending the unsteady Euler method of Choi and Kinnas (Journal of Ship Research, 2003) to include the effects of viscosity. The 3-D method will first be applied in the case of a (submerged) rectangular vertical plate subject to a horizontal sinusoidal inflow, since there are measurements of Sarpkaya (1996) available in this case. It should be noted that we plan on purchasing (with other available funds) a cluster of several CPUs in order to perform our calculations (especially in 3D) in parallel and thus reduce the run times significantly.
Anticipated Results
A robust, accurate, yet computationally efficient, model to predict the added mass and damping coefficients of FPSO hulls in roll, which will help understand and quantify the effectiveness of various bilge keel configurations in reducing roll motions.
Related Publications
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.
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.
Yu, Y.-H., Kinnas, S.A., Vinayan, V., Kacham, K., Modeling of Flow around FPSO Hull Sections Subject to Roll Motions: Effect of the Separated Flow around Bilge Keels, ISOPE 2005.
Vinayan, V., Kinnas, S.A., Yu, Y.-H., Modeling of the Flow Around FPSO Hull Sections to Roll Motions: Effects of Non-linear Boundary Conditions, OMAE 2005.
Kinnas, S.A., Vinayan, V, A BEM for the propagation of Nonlinear Free-surface waves, BeTeQ’05, 6th International Conference on Boundary Element Techniques, Montreal, Canada, July 2005.
