Progress Reports: December 2005 June 2005 December 2004 June 2004 December 2003 June 2003 December 2002 June 2002 December 2001FPSO Roll Motions
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 designAPPROACH: 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.
ANTICIPATED PROJECT DURATION: 3 years
PROJECT PLAN FOR YEAR 3 (2004-2005):Background: In 2003-2004, we applied the Navier-Stokes solver that we have been developing, on 2D FPSO hulls subject to roll motions with and without bilge keels. We also developed a 2-D panel method (employing the linearized free-surface conditions) to solve in the time domain for the inviscid flow around the same hull geometry. The latter method was used for comparison of the hull pressures and roll moment as predicted from the viscous and the inviscid methods. It was also used in order to validate the numerics of the employed finite volume method in the case without a bilge keel, as in that case the Euler solver (which is the same as the Navier-Stokes solver, except for the absence of viscous terms) should produce the same hull pressures and roll moment as those from the panel method. This validation test was very critical in helping us improve the current method. This test gave us guidance in improving the boundary conditions on the hull, and the pressure correction method (SIMPLE type). The final scheme allows for larger time steps (since it employs the unconditionally stable Crank-Nicholson scheme in time), and thus requires considerably less computer time to converge and produce a steady state roll moment distribution in time from which the hydrodynamic added mass and damping coefficients in roll can be extracted. Reducing the computing time is essential, especially when the method will be used to assess various bilge keel designs on actual FPSO hulls. The numerical tests also led us into the development of a scheme with a moving computational grid, as opposed to a stationary one (which was used originally) in which the motion of the hull was modeled through velocities on the hull which varied with time. Several grid dependence studies were performed and the effect of Reynolds number on the results was investigated in the case of a submerged hull. In conclusion, we now have a more robust numerical scheme. The above studies are described in the recent MS Thesis of Kacham, which can be downloaded (along with recent images from our research) from the following web site: http://cavity.ce.utexas.edu/kinnas/fpso
Scope of Work: In FY 2004-2005 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.
Prior Year Project Plans:
FY 2000-2001 Scope of Work: In FY1 of this 3-year project we have started the modeling of a 2-D hull section subject to prescribed roll motions. Our 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, we have started the 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).
In the second year we will continue with the implementation of the 2-D hull roll model, numerical convergence studies, and validations versus the results of other methods (based on full blown Navier-Stokes solutions ) and existing experiments (like those that were recently performed at UC Berkeley). In particular the added mass and damping coefficients will be evaluated in the present method by integration of the hull pressures to provide forces and moments, and then decomposition into the corresponding components. The effect of the position, shape, and height of the bilge keels on the hydrodynamic coefficients in roll will be studied. We will also continue with the modeling of the actual FPSO hull in roll motions using WAMIT, where now each of the sections of the hull will be analyzed using the 2-D hull model (with and without the bilge keels). The resulting 2-D hull coefficients will be integrated in a strip-wise sense in order to provide the correction to those coefficients determined by WAMIT (which does not include the effect of the separated flow behind the bilge keels). Finally, the current method will be validated using the data from the planned Experiments to be performed at OTRC under the companion project " FPSO Responses in Gulf of Mexico Environments" (by Dr. Ward)
FY 2002-2003 Scope of Work: In the current year of this project we have developed 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. The method was applied first in the case of an oscillating flat plate. In this case we also developed a laminar flow Navier-Stokes solver in which the non-slip conditions were applied on the plate. 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 are being studied in the case of heave and roll motions and comparisons with other methods are being carried out. The above methods and results will appear in the MS Thesis of K. Kakar, Ocean Eng. Group, UT Austin, August 2002 (under preparation). In addition we completed the 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).
In the next year we will continue with the systematic validation of the method in terms of grid dependence studies, and comparisons with an existing 2-D experiment. We will also perform parametric studies to study the effectiveness of the bilge keel with frequency for several plate lengths and locations along the bilge. In this year, we will also start the implementation of the 2-D hull results into WAMIT by modifying appropriately the 3-D added mass and damping coefficients of the hull by integrating the 2-D results along the hull (with and without the bilge keel). We will call this the 2 ½ D model. At this point the method should be applicable to 3-D hulls and could provide some valuable preliminary knowledge on the effectiveness of the bilge keels as a damping mechanism of the FPSO roll motions. This knowledge can be used to provide guidance on the design of the bilge keels to be implemented on the planned experiments on FPSO models at OTRC’s wave basin (by S. Ward). Simultaneously, we will start the extension of the 2-D method in 3-D. This should provide us with a more accurate predictive tool of the roll motions on an FPSO hull (including the effects of the lift on the bilge keels, which act like lifting surfaces). This extension will require considerable effort on the development of the appropriate cell distribution (in the transverse and axial direction), on the application of the linearized boundary conditions on the free surface, and on the numerical validation of the results. The development of a validated 3-D model will certainly require more time (at least one more year in addition to this one) to be completed, due to the significantly increased complexity of the model and the geometry, and the associated CPU time (despite the fact that this will be an Euler solver which can afford coarser grids than a RANS at the hull boundary and the free surface). The 3-D model will also provide valuable information on the validity of the 2 ½-D model, which is an approximation. The major effort in the development of the 3-D model within this year will consist of extending the formulation and implementation, performing initial validation tests (on axi-symmetric or simple 3-D geometries), and making the initial steps towards the application on hull geometries.
PRINCIPAL INVESTIGATOR (S) & OTHERS INVOLVED IN PROJECT:
PI(s): S.A. Kinnas
Others: R.S Mercier & E.G. Ward (PI on separate but related project FPSO Responses in Gulf of Mexico Environments).
Date: December 11, 2005Project Title: FPSO Roll Mitigation
MMS Project: 406 TO Numbers: 18033/35989
PI: Spyros A. Kinnas
COTR: A. Konczvald
Estimated Completion Date: 8/06
Project Description: Develop a computationally efficient finite volume method to study the unsteady flow around a 2-D hull section subject to roll motions with or without bilge keels. Evaluate the motions of an FPSO hull in the absence of the bilge keels (using WAMIT). Incorporate the effects of bilge keels on the FPSO hull by analyzing the hull sections using the developed 2-D analysis, and by determining the modified hydrodynamic coefficients using a strip theory type of approach. Investigate the effect of the location and extent of the bilge keels on the motions of an FPSO hull (supplied by Dr. Ward), and assess its effectiveness in mitigating roll motions.
Progress:
We continued with improvements of our methods for the prediction of the hydrodynamic coefficients in roll of FPSO hull sections. Our viscous method (NS-2D) was tested with the commercial viscous flow code (Fluent) in the absence of a free-surface, in the case of a hull (without or with bilge keels) subject to a sinusoidal horizontal inflow, and our results (pressure distributions and forces) were found to be in good agreement with those of Fluent. More recently we have started incorporating the non-linear free-surface conditions in our viscous flow solver (NS-2D). In our inviscid non-linear approach we improved the panel method by introducing linear “saw-tooth” corrections to account for the difference of the actual solution from the approximated piecewise constant over each panel. Those corrections were accounted for in an iterative sense. It was found, as expected, that the corrections improved the accuracy of the solution significantly at the “corners” of the domain (e.g. free-surface/body intersection and upstream or downstream boundary/free-surface intersection). The method was tested by applying it to some non-linear Stokes waves. It should be noted that our inviscid non-linear method has helped us a lot in validating our viscous flow method (NS-2D) in the limit of no viscosity, as well in assessing the effect of the non-linear free-surface conditions on the results. For details see the supplied references.
Finally, we used the added mass and damping coefficients as predicted from our methods in order to predict the response of a typical FPSO hull to monochromatic beam seas, in the case of a smooth hull or one supplied with bilge keels. The results of this latest study can be summarized as follows:
• The effectiveness of the bilge keels is clearly illustrated in these Figures. In some cases, there was a 50% reduction in the RAO with a bilge keel length of 2%B and a 70% reduction with a 4% bilge keel. In other words, for the FPSO hull we studied and the Froude no. of 0.6 a roll amplitude of 20 degrees in a bare hull, will be reduced to 14 degrees with a 2% bilge keel length, and to 10 degrees with 4% bilge keel length.
• The effectiveness of the bilge keels in mitigating roll motions cannot be accurately predicted by the inviscid codes. This is due the fact that viscous effects in the vicinity of the bilge keels, which are not captured by the inviscid codes, play a major role in increasing the damping coefficient and hence decreasing the roll motion.
Reports & Publications:
[1] Yu, Y.-H., Kinnas, S.A., Vinayan, V., and Kacham B., "Modeling of Flow Around FPSO Hull Sections Subject to Roll Motions: Effect of Separated Flow around Bilge Keels," The 15th International Offshore and Polar Engineering Conference (ISOPE), Seoul, Korea, June 19-24, 2005.
[2] Vinayan, V., Kinnas, S.A., and Yu, Y.-H., "Modeling of Flow Around FPSO Hull Sections Subject to Roll Motions: Effects of Non-linear Boundary Conditions," 24th International Conference on Offshore Mechanics and Arctic Engineering (OMAE), Halkidiki, Greece, June 12-16, 2005.
[3] Kinnas, S.A. and Vinayan, V. "A BEM for the propagation of non-linear free-surface waves," BeTeq 2005, 6th International Conference on Boundary Element Techniques, Montreal, Canada, July 27-29, 2005 (invited paper).
Date: June 2005
Project Title: FPSO Roll Mitigation
MMS Project: 406 TO Numbers: 18033/35989
PI: Spyros A. Kinnas
COTR: A. Konczvald
Estimated Completion Date: August, 2005
Project Description: Develop a computationally efficient finite volume method to study the unsteady flow around a 2-D hull section subject to roll motions with or without bilge keels. Evaluate the motions of an FPSO hull in the absence of the bilge keels (using WAMIT). Incorporate the effects of bilge keels on the FPSO hull by analyzing the hull sections using the developed 2-D analysis, and by determining the modified hydrodynamic coefficients using a strip theory type of approach. Investigate the effect of the location and extent of the bilge keels on the motions of an FPSO hull (supplied by Dr. Ward), and assess its effectiveness in mitigating roll motions.
Progress: In the last 5 months, we focused on the prediction of the pressure distributions along the surface of an FPSO hull using our methods, and on the refinement of our algorithm for the propagation of non-linear free-surface waves. Details of our investigation and results are presented in the three papers which are listed at the end of this report.
Grid-dependence studies were performed in regards to the predicted pressure distribution in the vicinity of the bilge keel of an FPSO hull subject to forced roll motions. In the case of our Navier-Stokes solver, we were able to establish an acceptable grid resolution that would produce reliable pressure distributions in the vicinity of the bilge keel (see [1] for details). In the BEM solver, we studied the performance of three different approaches:
As reported in [2], we found that the pressure distributions (in the vicinity of the bilge keels in particular) were very close to each other as predicted by the MBLF and the NL schemes, for small to moderate angles of roll, while the pressures as predicted by L were considerably different from the rest (even for very small roll angles). It should be noted that the predicted time history of the roll moment (also the added mass and damping coefficients) were negligibly affected by the 3 schemes. This study helped us establish that it was essential that we apply the non-linear boundary conditions on the moving body.
- L: linear, in which the linearized boundary conditions are applied on the free-surface as well as on the body boundary,
- MBLF: where the non-linear boundary conditions are applied on the moving hull boundary (MB), while the linearized boundary conditions are still applied on the free-surface (LF), and
- NL: where the non-linear boundary conditions are applied on both the moving hull boundary, as well as on the free-surface.
In our most recent Navier-Stokes solver we actually employ conditions similar to those of MBLF in the BEM solver (in the past we also applied the L scheme in the N-S solver). The difference in the pressure distributions between the L and MBLF schemes also explains the considerably different added mass and damping coefficients as predicted by the Navier-Stokes solver (as reported in the MS Thesis of Kacham, UT, August 2004), with the ones predicted by our newest MBLF scheme being considerably closer to those measured in experiments (see [1] for details).
We are currently working on refining our fully non-linear BEM scheme [3] in the case of extreme angles of roll (20 degrees or higher), so that we can complete the comparative study of the results from the various schemes (L, MBLF, and NL). In addition, we are modifying our Navier-Stokes solver in order to achieve reliable solutions with larger time steps, in order to improve computational efficiency, or allow for even more refined mesh than currently used.
Reports & Publications:
[1] Yu, Y.-H., Kinnas, S.A., Vinayan, V., and Kacham B., "Modeling of Flow Around FPSO Hull Sections Subject to Roll Motions: Effect of Separated Flow around Bilge Keels," The 15th International Offshore and Polar Engineering Conference (ISOPE), Seoul, Korea, June 19-24, 2005 (accepted).[2] Vinayan, V., Kinnas, S.A., and Yu, Y.-H., "Modeling of Flow Around FPSO Hull Sections Subject to Roll Motions: Effects of Non-linear Boundary Conditions," 24th International Conference on Offshore Mechanics and Arctic Engineering (OMAE), Halkidiki, Greece, June 12-16, 2005 (accepted).
[3] Kinnas, S.A. and Vinayan, V. "A BEM for the propagation of non-linear free-surface waves," BeTeq 2005, 6th International Conference on Boundary Element Techniques, Montreal, Canada, July 27-29, 2005 (invited paper, under preparation).
Date: December, 2004
Project Title: FPSO Roll Mitigation
MMS Project: 406 TO Numbers: 18033/35989
PI: Spyros Kinnas
COTR: A. KonczvaldEstimated Completion Date: 12/31/05
Project Description: Develop a computationally efficient finite volume method to study the unsteady flow around a 2-D hull section subject to roll motions with or without bilge keels. Evaluate the motions of an FPSO hull in the absence of the bilge keels (using WAMIT). Incorporate the effects of bilge keels on the FPSO hull by analyzing the hull sections using the developed 2-D analysis, and by determining the modified hydrodynamic coefficients using a strip theory type of approach. Investigate the effect of the location and extent of the bilge keels on the motions of an FPSO hull (supplied by Dr. Mercier), and assess its effectiveness in mitigating roll motions.
Progress: In the last 6 months, we continued with the systematic study of the numerics of our method, first in the case of a fully submerged hull. In this way, the additional complexity of the free surface was factored out. In particular we compared the pressure distribution along the hull surface as predicted by the present method and a boundary element method (developed in the beginning of this year). These comparisons led us to the introduction of the moving grid, as opposed to using a fixed grid on the hull mean location, which was found capable of producing a very good agreement of the results from our method (in the absence of viscosity) with those of the potential method. We then included the effects of the moving grid in the Navier-Stokes equations. The effects of the Reynolds number on the pressure distribution were thus studied and it was found that they were significant only for very small Re numbers (if the order of 1000).
We then applied the most recent method to the case of a hull with and without bilge keels and for various Froude numbers. The newest results, the added mass and damping coefficients were compared with measurements and other numerical results, and were found to be in good agreement. The effect of the bilge keel orientation (horizontal, vertical, and at 45 degrees) was then studied and preliminary results showed trends similar to those measured as well those computed from another method, despite the fact that our bilge keel shape was not the same to that tested.
We finally modified our boundary element method (BEM) by incorporating the fully non-linear free-surface conditions. This will help us quantify the effects of the currently used simplified linearized free surface conditions in our finite volume method. In fact some preliminary results have shown that at larger angles of roll (20 degrees amplitude) the effects of non-linear free surface conditions on the hydrodynamic coefficients can be important. It was found that the predicted pressures using non-linear vs. linear differ can differ considerably even at small amplitudes of roll (even though the integrated roll moments are very close to each other), and that should certainly affect the behavior of the viscous solution and its effect on the pressure distribution. Finally, it was found that the predicted profiles starboard and portside of the FPSO hull are NOT anti-symmetric in non-linear theory, and this seems to be consistent with observations.
Date: June 13, 2002Date: June 2004
Project Name: FPSO Roll Motions
Project Number: 406 Task Order: 18033
Principal Investigators: Spyros A. Kinnas
Estimated Completion Date: September 2005
Project Description: Develop a computationally efficient finite volume method to study the unsteady flow around a 2-D hull section subject to roll motions with or without bilge keels. Evaluate the motions of an FPSO hull in the absence of the bilge keels (using WAMIT). Incorporate the effects of bilge keels on the FPSO hull by analyzing the hull sections using the developed 2-D analysis, and by determining the modified hydrodynamic coefficients using a strip theory type of approach. Investigate the effect of location and size of bilge keels on the motions of an FPSO hull from OTRC model test data, and assess its effectiveness in mitigating roll motions.
Progress: The development and numerical tests of the finite volume method in the case of a vertical plate and an FPSO hull with and without the bilge keels is continuing.
The new finite volume method, including the viscous effects, has been applied to an FPSO hull subjected to heave and roll motions. Heave results compared satisfactorily to the earlier experiments (Vugts). Roll motions for an FPSO hull without and with bilge keels were computed over a large range of Froude numbers using linearized free surface and body boundary conditions. The resulting hydrodynamic coefficients were compared with existing experimental values. The added mass and damping coefficients predicted by the Navier Stokes solver (including the viscous effects) were over-predicted at low Froude numbers, and were not a significant improvement over predictions by the Euler solver (inviscid) or the BEM method results. Pressure distributions on the hull predicted with and without viscous terms exhibited some unrealistic oscillatory behavior in the bilge keel region, prompting the need for using finer grids (as discussed below).
The stability of the solver in the numerical scheme has been improved by implementing a fully implicit scheme in time. Improved treatments of the non-linear terms of the Navier-Stokes or the Euler equations and the development of a consistent pressure-correction method have improved the performance of the scheme significantly. The present scheme allows for larger time steps for a fixed grid, or, most importantly, for a fixed time step the scheme allows for much finer grids. Using finer grids has reduced previous discrepancies between predictions and experimental results for flow paste a vertical plate at higher Keulegan-Carpenter numbers. The current scheme also allows us to simulate the FPSO hull problem with much finer grids near the bilge keels. All improvements in the numerical scheme verified well against the step function problem, the tunnel flow or the alternating flow past a cylinder. All improvements of the numerical scheme are now being extended to the vertical plate and FPSO motion cases. These improvements should provide more accurate predictions and improved agreement with experimental data for flows past a vertical plate the higher KC number, and allow the use of finer grid to study the FPSO hull with bilge keels.
It should also be noted that the ability to use larger time steps will decrease computational times significantly (faster by an order of 10 times or more). This is important for the 2-D FPSO runs, which required about 5-6 hours for a moderate grid, and will be essential as the method is extended to 3-D.
The development of the panel method in time (using linearized free-surface conditions) for the study of the 2-D hull in heave or roll has been critical in helping us validate the numerics of the finite volume method. In addition, the panel method is currently extended to allow for non-linear free-surface conditions, and will be used to estimate the error introduced by the linearized free-surface conditions, which are currently applied in our solution scheme.
We will continue this systematic study and validation of the results of our method over the summer.
We also plan to compare predictions with experimental data from (1) an FPSO model test in the OTRC basin and (2) water velocity measurements (PIV) in the flow field around a 2D hull subjected to roll in a TAMU flume.
Reports and Publications: None
Date: December 2003
Project Name: FPSO Roll Motions
TEES Project Number: 32558-5888A1 MMS Task Order: 18033 MMS Project Number: 406
Principal Investigators: Spyros A. Kinnas
Estimated Completion Date: December 2005
Project Description:
Develop a computationally efficient finite volume method to study the unsteady flow around a 2-D hull section subject to roll motions with or without bilge keels. Evaluate the motions of an FPSO hull in the absence of the bilge keels (using WAMIT). Incorporate the effects of bilge keels on the FPSO hull by analyzing the hull sections using the developed 2-D analysis, and by determining the modified hydrodynamic coefficients using a strip theory type of approach. Investigate the effect of the location and extent of the bilge keels on the motions of an FPSO hull (supplied by Dr. Ward), and assess its effectiveness in mitigating roll motions.
Progress:
We continued with the development and numerical tests of the finite volume method in the case of a vertical plate and an FPSO hull with and without bilge keels.
In the case of flat plate, we have made several sensitivity studies with respect to the time step size and the grid size. It was found that modeling the exact geometry of the plate (instead of using a plate with thickness that of one cell) improved the convergence of the results of our method. A 60-degree angle (the same as that in the experiment of Sarpkaya) was used to model the tip of the plate. To avoid applying the boundary conditions at sharp corners we decided to move from the current node-based to a cell-based finite volume scheme. In addition, an improved pressure correction scheme and an implicit method in time were incorporated. The method was tested in the cases of viscous Couette flow or the through-flow past a plate and the expected flow fields (in terms of velocity and pressure distributions) were recovered. In the case of oscillating flow past a flat plate at Keulegan-Carpenter number of KC=1 results were produced for low and high Reynolds numbers and the results were found to be unstable in the case of the higher Re numbers (when the convective terms of the Navier-Stokes equations become more important). We are still in the process of investigating the cause of instability of the results of our method in the case of higher Re numbers. Once the 2-D method is functional (in the case of low as well as high KC and Re numbers) we plan on extending it to 3-D, and on doing comparisons versus the measurements of Sarpkaya in the case of 3-D (square) plates.
In the case of an FPSO hull section the most recent version of our method (with the improvements as described in the previous paragraph) has been implemented using the linearized free-surface conditions. A new grid algorithm has been developed which allows for denser cell distributions near the hull and the bilge keels. The scheme has been tested in the case of the though-flow of a progressive wave past a 2-D hull and the expected flow filed (in terms of velocity and pressure) has been recovered. We are currently testing the case of the FPSO hull subject to heave and roll motions, without and with bilge keels. At the same time we have developed a 2-D boundary element method which deals with the attached flow around an FPSO hull section, without or with a bilge keel. The method was applied to the sections of a 3-D FPSO hull-like geometry with and without bilge keels by using strip theory, and by applying WAMIT on the 3-D hull geometry. The discrepancies of the strip theory vs. the 3-D method, in the case of potential flow, were thus quantified. We plan on using the FPSO hull geometry which was used in recent experiments performed at OTRC’s Wave Tank in order to make comparisons of results from the potential and viscous flow methods with the data from a roll-decay experiment.
Reports & Publications:
Kinnas, S.A., Yu, Y-H, Kacham, B., and Vimal, V., “Modeling of the Separated Flow over Bilge Keels of FPSO Hulls under Heave and Roll Motions”, ISOPE-2004, May 23-28, 2004, Toulon, France, abstract accepted, paper under preparation.
Date: June, 2003
Project Name: FPSO Roll Motions
Project Number: 5888A1 Task Order: 18033
Principal Investigators: Spyros A. Kinnas
Estimated Completion Date: 12/31/03
Project Description:
Develop a computationally efficient finite volume method to study the unsteady flow around a 2-D hull section subject to roll motions with or without bilge keels. Evaluate the motions of an FPSO hull in the absence of the bilge keels (using WAMIT). Incorporate the effects of bilge keels on the FPSO hull by analyzing the hull sections using the developed 2-D analysis, and by determining the modified hydrodynamic coefficients using a strip theory type of approach. Investigate the effect of the location and extent of the bilge keels on the motions of an FPSO hull, and assess its effectiveness in mitigating roll motions.
Progress:We continued with the development and numerical tests of the finite volume method in the case of a vertical plate and an FPSO hull with and without bilge keels. In the case of the flat plate comparisons of detailed time histories of the flow-fields and the vorticity fields, as predicted by the present Euler and the Navier-Stokes method, in the vicinity of the flat plate were made in the case of low (KC=1) and high (KC=10) Keulegan-Carpenter numbers. The flow-fields were found to be quite similar at the low KC and less similar at the high KC number. In addition, the vorticity patterns shed from the tip of the plate seemed to be similar to those observed in the experiment of Sarpkaya and O’Keefe (1995). The results of the present Navier-Stokes method were also compared with those of a commercial code (Fluent) and found to be in good agreement.
In the case of an FPSO hull the current (Euler) method was applied in the case of 2-D hull section with and without bilge keels. In the case of the hull without the bilge keels the results were found to be in good agreement to those of potential theory (as they should since in the case of a hull without a bilge keel the Euler and potential flow methods should produce the same answer), but the added mass coefficient in Roll was over-predicted when compared to those measured by Vugts (as expected). It should be noted that in the case of heave the added mass and damping coefficients were in very good agreement with those measured by Vugts. In the case of a hull with bilge keels the current (Euler) method was found to over-predict the added mass and the damping coefficients in roll, despite the fact that the present method predicts the expected increase of the hydrodynamic coefficients with bilge keel size. We are presently extending our finite volume method (using the linearized free-surface conditions) to include the viscous terms in the Navier-Stokes equations. The method will be applied in the case of FPSO hull sections with and without bilge keels and comparisons with the above-mentioned experiments will be done. Using Fluent, we have studied the effect of Reynolds number in the case of turbulent flow over a 2-D hull section with bilge keels, subject to alternating rotating flow in the absence of a free-surface. The results showed very small effect of the Reynolds number on the roll moment over a large range of Reynolds numbers (from 800-100,000).
Once our Navier-Stokes method has been implemented in the case of 2-D hulls with and without bilge keels, and the convergence and validation studies have been completed, the application of the results from 2-D (via a strip theory approach) to 3-D Hulls will be studied. Later, the method will be extended to apply on 3-D hull and bilge keel geometries. Our methods and results have been reported in the two publications (see below), and some were also presented at the International FPSO Forum hosted by OTRC on May 1, 2003.
Reports & Publications:
Kinnas, S.A., Yu, Y-H, Kacham, B. and Lee, H.S., “A model of the flow around bilge keels of FPSO hull sections subject to roll motions”, Proceedings of the 12th Offshore Symposium, Texas section of the SNAME, February, 2003, Houston, Texas
Kinnas, S.A., Yu, Y-H, Lee, H.S., and Kakar, K., “Modeling of Oscillating Flow Past a Vertical Plate”, ISOPE, May, 2003, Honolulu, Hawaii
OTRC PROJECT STATUS REPORT
Date: 12/21/2002Project Name: FPSO Roll Motions
Project Number: 5888A1 Task Order: 18033
Principal Investigators: Spyros A. Kinnas
Estimated Completion Date: 12/31/03
Project Description: Develop a finite volume method to study the unsteady flow around a 2-D hull section subject to roll motions with or without bilge keels. Evaluate the motions of an FPSO hull in the absence of the bilge keels (using WAMIT). Incorporate the effects of bilge keels on the FPSO hull by analyzing the hull sections using the developed 2-D analysis, and by determining the modified hydrodynamic coefficients using a strip theory type of approach. Investigate the effect of the location and extent of the bilge keels on the motions of an FPSO hull (supplied by Dr. Ward), and assess its effectiveness in mitigating roll motions.
Progress: The development of the finite-volume based Euler solver continued with the inclusion of the effects of free-surface, by applying the linearized dynamic and kinematic boundary conditions. It was found that a radiation condition (required in the case of panel method formulations) was not necessary in our case. In addition, the extent of the computational domain had to be adjusted depending on the wave length for the frequency under consideration. The method was validated extensively and systematically, by first recovering the well known solution of a plane progressive wave, and then by comparisons of the added mass and damping coefficients with those of Vugts in the case of heave motions of a rectangular hull section (without bilge keels), for a wide range of reduced frequencies. Grid sensitivity studies were also performed, and more are being carried out currently, especially in the case of roll motions of rectangular hull sections with bilge keels. Results were also compared with those of Yeung, and are being currently compared with the existing measurements of Webster et al.
The same method has also been applied in the case of oscillating flow past a vertical flat plate, in order to simulate the experiment of Sarpkaya. In this case the laminar Navier-Stokes equations have also been solved by applying the no-slip conditions on the flat plate. The predicted drag and the inertia moment coefficients, from the numerical solution of the Euler and the Navier-Stokes equations, have been compared with each other and with those measured by Sarpkaya, over a wide range of Keulegan-Carpenter numbers. The Euler and the Navier-Stokes methods seem to predict hydrodynamic coefficients which are close to each other and also close to the measured. We currently use the flat plate problem in order to perform systematic convergence studies of the results (with grid size and time step), and detailed comparisons between the results form the Euler and the Navier Stokes equations (especially in terms of the vorticity distribution in the vicinity of the tip of the plate) which should help us understand better the numerics of the method and improve its computational efficiency.
Once the above convergence and validation studies in 2-D have been completed, the application of the results from 2-D (via a strip theory approach) to 3-D Hulls will be studied. Later, the method will be extended to apply on 3-D hull and bilge keel geometries. The above have been reported in Kakar’s thesis (supervised by Kinnas), and a paper which will be presented at the ISOPE 2003 meeting in Honolulu. The method and results were also summarized by Dr. Ward in a recent FPSO workshop in Spain.
Reports & Publications:
“Computational Modeling of FPSO Hull Roll Motions and Multi-Component Marine Propulsion Systems,” by K. Kakar, Masters Thesis, The University of Texas at Austin, August 2002.
“Computational Modeling of FPSO Hull Roll Motions,” by Kakar and Kinnas, ISOPE 2003, Honolulu, July 2003 (under preparation).
OTRC PROJECT STATUS REPORTS
Project Name: FPSO Roll Motions
Task Order: 18033 Project Number: 5888A1
Principal Investigators: Spyros A. Kinnas
Estimated Completion Date: 12/31/02
Project Description: Develop a finite volume method to study the unsteady flow around a 2-D hull section subject to roll motions with or without bilge keels. Evaluate the motions of an FPSO hull in the absence of the bilge keels (using WAMIT). Incorporate the effects of bilge keels on the FPSO hull by analyzing the hull sections using the developed 2-D analysis, and by determining the modified hydrodynamic coefficients using a strip theory type of approach. Investigate the effect of the location and extent of the bilge keels on the motions of an FPSO hull (supplied by Dr. Ward), and assess its effectiveness in mitigating roll motions.
Progress: The finite-volume based Euler solver developed has been applied to study heave and roll motions for a rectangular barge section. Results for the barge section (without bilge keels) undergoing heave motion have been compared to results presented by Vugts and the hydrodynamic coefficients obtained show good correspondence. Presently, the force histories and hydrodynamic coefficients for roll motions are being compared to results presented by Yeung et al. A new boundary condition, based on linear wave theory, for the x- and y-direction velocities at the free surface is being experimented with and it is hoped that this, combined with a radiation condition, would allow us to effectively capture the free surface. Also, a study of the hydrodynamic coefficients over a range of exciting frequencies will be conducted.
In order to validate our basic assumption that viscous effects are unimportant for strongly separated flows, as are seen past bilge keels, a finite-volume method based laminar unsteady Navier-Stokes solver has also been developed. After sufficient numerical validation and convergence studies, this has been applied to study the separated flow past flat plates under two different conditions - one with a fixed plate subject to an oscillating flow and the other with an oscillating plate in an unbounded fluid domain. The same problem is solved using the unsteady Euler solver and the preliminary comparisons of the force history plots are encouraging and confirm our assumption that an Euler solver captures most of the effects. It is planned to extend this comparison to hulls undergoing heave and roll motions.
Reports & Publications:
'Modeling Roll Motions of an FPSO Hull using an Unsteady 2-D Euler solver, by K. Kakar, presented at the Joint MTS/SNAME Meeting at Texas A&M University, March 27, 2002'Real-time Visualization of Hull/3-D Waves Interaction, by A. Hariramasamy and S. Natarajan, presented at the Joint MTS/SNAME Meeting at Texas A&M University, March 27, 2002
'Computational Modeling of FPSO Hull Roll Motions and Multi-Component Marine Propulsion Systems', by K. Kakar, Masters Thesis, The University of Texas at Austin, expected August 2002 (under preparation).
OTRC PROJECT STATUS REPORTS
Project Name: FPSO Roll Motions
Task Order: 18033 Project Number: 5888A1
Principal Investigators: Spyros A. Kinnas
Estimated Completion Date: 12/31/02
Project Description: Develop a finite volume method to study the unsteady flow around a 2-D hull section subject to roll motions with or without bilge keels. Evaluate the motions of an FPSO hull in the absence of the bilge keels (using WAMIT). Incorporate the effects of bilge keels on the FPSO hull by analyzing the hull sections using the developed 2-D analysis, and by determining the modified hydrodynamic coefficients using a strip theory type of approach. Investigate the effect of the location and extent of the bilge keels on the motions of an FPSO hull (supplied by Dr. Ward), and assess its effectiveness in mitigating roll motions.
Progress: The finite-volume method to study method has been formulated and implemented on a 2-D hull shape with and without bilge keels. The model applies a linearized free surface condition, as well as a linearized kinematic boundary condition on the hull (i.e. the conditions on the hull are applied on its mean position). The model has been found capable of predicting the expected separated flow in the vicinity of the bilge keel. The numerics of the method (grid and time step size) were first validated against known results in the case of an unsteady flow past a “transparent” boundary, and a cylinder subject to a sinusoidal horizontal gust. We currently study the effect of grid refinement on the results (vorticity distributions, and resulting hydrodynamic coefficients) in the case of a 2-D hull section with and without bilge keels. At the same time we have imported successfully a FPSO hull geometry (supplied by Dr. Ward) into WAMIT and have evaluated the 3-D hull motions for given wave environment. We have also performed convergence studies to assess the effect of panel size on the results.
Reports & Publications: “An Unsteady Finite Volume Method for the Prediction of the Flow about 2-D Hull Section Subject to Roll Motions With and Without Bilge Keels”, OTRC Report, by K. Kakar and S.A. Kinnas (under preparation).