fpso roll mitigation

FPSO Roll Mitigation (Kinnas)

MMS/OTRC Review Meeting - UT Austin 1

FPSO Roll MitigationPI: 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



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



Objective:Develop robust, validated

computational model to study effect of bilge keel shape on

roll motions



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) .



Today’s Presentation

Part I: Modeling of the Unsteady Separated Flow over Bilge Keels of FPSO Hulls under Heave and Roll Motions ~ Finite Volume Method (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



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)



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



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 MethodCollocated variable, non-staggered grid arrangement,

Non-orthogonal grids

21( ) , 0

Re

UUU P U U

t

U, V, P

Cell Based



• 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’face is the velocity correction term, әp’ /әn is 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.

11

, , 2

n nn ni j i j

f fU U t

*

* *

*

,

'

'

face face face face

faceface face

p p p

pV V V V t

np

t ds V dsn



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

( ) ( )grid grid

u u u uu v

t t x y

/u t

21( ) ( ) ( )

Regrid grid

U U Uu v UU P U

t x y

• Moving Grid

gridu

gridv

/U t



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).



Previous Results• Oscillating Flow Past a 2-D Vertical Plate



• Drag & Inertia Coefficient for a Range of Kc=UmT/h (0.5 < Kc < 5)

2

20

ˆ3 ( ) cos

4dm

FC d Drag coefficient

hwU

2

3 20

ˆ2 ( )m

m

KC F sinC d Inertia coefficient

hwU



The pressure distribution along the submerged hull without

bilge keels

• 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)

FVM (Inviscid) Potential Solver

/ / ( )( / ) ( )( / )n n n S S nP n U t U Ugrid U n U Ugrid U S

:

: ,

Invicid Free slip boundary condition

Viscous U V velocity of the moving body

S



Pressures on submerged hull with bilge keels Effect of Reynolds number

t/T=0.25 t/T=0.50



Grid used by Kakar, MS 2002, UT Austin

• FPSO Hull Subject to Roll Motions

Grid improved by Kacham, MS 2004, UT Austin

B=2b



Comparison of damping coefficients from previous solver and other results,

: ; : ; :

bFroude Number Fn

g

Angular frequency b half beam length g gravity

Comparison of added mass coefficients from previous solver and other results

• Added Mass and Damping Coefficients of FPSO Hull without Bilge Keels -Without moving grid

Kacham, MS 2004, UT Austin



Comparison of added mass 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

Comparison of damping coefficients from the previous solver and other results



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.



• FPSO Hull Subject to Roll Motions

θ

θ=20° θ=45° θ=70°

Bilge Keels width (length)



Time

Mo

me

nt

0.1 0.2 0.3 0.4 0.5-0.1

-0.05

0

0.05

0.1 Area=3.95x10-6, t=10-3

Area=4.43x10-5, t=10-2

• Convergence Study in Space and in TimeFn=1.0, 2% Bilge Keels

Min Area=4.43x10-5

t=10-2

Min Area=3.95x10-6

t=10-3



θ=45°

% Fnof Bilge Keels

0.6 0.8 1.0 1.2

0%a66 0.0606 0.0398 0.0327 0.0312

b66 0.0175 0.0265 0.0237 0.0200

2%a66 0.0674 0.0465 0.0376 0.0365

b66 0.0289 0.0358 0.0336 0.0309

4%a66 0.0702 0.0520 0.0457 0.0432

b66 0.0437 0.0481 0.0436 0.0441

• Table of Added Mass and Damping Coefficient



Comparison of added mass coefficients from the present solver and other results

• Added Mass and Damping Coefficients of FPSO Hull Subject to roll motions

Comparison of damping coefficients from the present solver and other

results



• 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.



• The vorticity contour plot of a FPSO hull with 4% bilge keels subject to the roll motion at Fn=0.6.

X

Y

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

VOR

20181614121086420

-2-4-6-8-10-12-14-16-18-20

t = 2.500

Vorticity Contour Plot

X

Y

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

VOR

20181614121086420

-2-4-6-8-10-12-14-16-18-20

t = 2.750

Vorticity Contour Plot



a6

6&

b6

6

0 10 20 30 40 50 60 70 80 90

0.036

0.038

0.04

0.042

0.044

0.046

0.048

0.05

a66b66

Comparison of added mass and damping coefficients between different angles of 4%

bilge keels with Fn=1.0

Angle of Bilge Keels

θ=45° θ=20° θ=70°

Fn

%of Bilge

Keels

1.0 1.0 1.0

4%

a660.0457 0.0488 0.0496

b660.0436 0.0404 0.0391

• Added Mass and Damping Coefficients at Different Angles of Bilge Keels

Similar trend to that in Na 2002 and Yeung 2003.



• The vorticity contour plot of FPSO hulls with 4% horizontal or vertical bilge keels subject to the Roll motion at Fn=1.0.



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).



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.



Part IIApplication of Panel Method to 2-D

FPSO Hulls Subject to Roll Motion

Vimal Vinayan (Ph.D. student)



Mathematical Background

• Potential Flow (Inviscid / Irrotational)

• Green’s Second Identity

on simplification,

• Navier-Stokes Equations



Mathematical Background Contd..



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



Mathematical Background Contd..• Boundary Condition : H

• Kinematic Boundary Condition



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)



Forces and Moments• Pressure (Hull)Dynamic Pressure

Hydrodynamic Coefficients



Numerical Formulation Contd..• Time Stepping – Modeling of Free Surface

Mixed Eulerian – Lagrangian (MEL) Method of Longuet-Higgins and Cokelet (1976)

2

( , )

and

1

2 y x t

x

F Gy

g

DFG

Dt

• 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)



Results – Roll (5o Roll)

Moment history

• Roll amplitude of 5 degrees

• Comparison of results for Linear and Nonlinear algorithms




Moment history






Pressure Distribution





Results - RollWave Elevation (50 Roll)



Results - Roll

Wave Elevation (50 Roll)

NOTE: Non-linear wave profiles are NOT (stbd/port) anti-symmetric




NOTE: Non-linear wave profiles are NOT (stbd/port) anti-symmetric



Non-linear Results – Roll Hull Motion and Wave Elevation (200 Roll)



Non-linear Results - RollHull Motion and Wave Elevation (200 Roll)

NOT to scale!



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

fpso roll mitigation

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