how to estimate hydrodynamic coefficients applicable for lifting

Classification: Internal Status: Draft

Finn Gunnar Nielsen, Chief Researcher StatoilHydro Research Centre, Bergen

How to estimate hydrodynamic coefficients applicable for lifting from the sea bed.

Subsea Lifting OperationsKranteknisk ForeningTekniske foreningers servicekontorStavanger, 27. 28. november 2007

2Hydrodynamic coefficients for subsea structuresContent Hydrodynamic mass and damping

Crossing of the splash-zone.

Deeply submerged.

Landing on bottom.

Estimating hydrodynamic coefficients Tabulated values

Simple estimates

Advanced methods

Simulation challenge during lift-off. Example

3Phases of the installation process1. Lift-off from deck.2. Lift in air3. Crossing splash zone.4. Lowering through the water column5. Landing the structure.

12

3

4

5

4Subsea template Ormen Lange

L * B * H =

44m *33m *15m

M=1150*103 kg

5Added mass for simple 2Dforms

Challenge:How to relate such values to real structures?

Key issues:InteractionShieldingPerforationFinite lengthViscous effectsFree surface proximityBottom proximity

Source: DNV RP C205

6Natural periods (Lightly damped)

Pendulum in air:

Pendulum in water:

( )111 2

m A LT

mg gV

+= ( )22

2 2m A L

Tmg gV

+=

( )333 2

Em A LTEA

+=

1,2 2LTg

=

3 2 EmLTEA

=

1, 2

3

7Added mass versus damping ? Oscillation of a body in calm water: Added mass:

Force on body in phase with acceleration

Damping: Force on body in phase with velocity ( ) 1 2F m A x B x B x x= + + +

0 5 10 15 20 25 30 35 40 45 50-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (sec)

F

t

o

t

PositionForce

Position and total force

0 5 10 15 20 25 30 35 40 45 50-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (sec)

F

o

r

c

e

ForceAdded mass force

Total force and added mass contribution

8Added mass versus damping ?

( ) 1 2F m A x B x B x x= + + +

0 5 10 15 20 25 30 35 40 45 50-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (sec)

F

t

o

t

PositionForce

Position and total force Total force and linear damping force

0 5 10 15 20 25 30 35 40 45 50-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (sec)

F

o

r

c

e

ForceLinear damping

Oscillation of a body in calm water: Added mass:


Damping: Force on body in phase with velocity

9Added mass versus damping ?

( ) 1 2F m A x B x B x x= + + +

0 5 10 15 20 25 30 35 40 45 50-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (sec)

F

t

o

t

PositionForce

Position and total force Total force and quadratic damping force

0 5 10 15 20 25 30 35 40 45 50-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (sec)

F

o

r

c

e

ForceDrag force

Oscillation of a body in calm water: Added mass:


Damping: Force on body in phase with velocity

10

Water entry of TOGP template (2000)

11

Water entry forces, calm water

Vertical hydrodynamic force (positive upwards):

Note: A33 from high frequency limit

V

2333 33h z z

dAF gV A U Udh

= + +

z

xz = 0

h

Uz

Hydrostatic Added mass SlammingWater entry

12

Water entry forces, including waves

Vertical hydrodynamic force:

z

x

V

z = 0 h

( ) ( )( ) ( )

2333 33

1 2

hdAF gV V Adh

B B

= + + + + +

Water entry termPosition dependent added mass

13

Added mass for simple structures.Horizontal circular cylinder

-1 -0.5 0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 Added mass for horizontal 2D cylinder. = 0 at z = 0

Submergence h/r

A

3

3

/

r

2

Analytical expressionsAsymptotic values

-1 -0.5 0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Derivative of A33 for horizontal 2D cylinder.

= 0 at z = 0

Submergence, h/r

(

d

A

3

3

/

d

h

)

r Numerical differentiationAsymptotic value

h

2R

=0

3

14

Close to bottom No action from waves Modified water entry / slamming term Added mass for body close to fixed wall (Zero frequency limit)

15

Vertical force close to bottom

2333 33 3 3

1 3 2 3 3

0.5=

hdAF gV Adh

B B

h

2R

3

33 0dAdh

16

A33 2D cylinder close to bottom

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 30

0.5

1

1.5

2

2.5Added mass for horizontal 2D cylinder. d/dz = 0 at z = 0

Centre distance from wall h/r

A

3

3

/

r

2

2/3-1

17

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 51

1.5

2

2.5

3

3.5

4

4.5

5

h/R

A

3

3

/

R

3

WAMIT results for t/R=0.05Asymptotic results for h/R1

Circular disc close to bottom

Far from bottom h/R >>1:

Close to wall (Vinje 2001):

333

83

A R=

33 as h 0A

18

Perforated plate, circular hollows, potential theory Plate L*B = 15m*10m

(0) 233 0.625A LB=

19

Suction anchor Fully submerged, no ventilation (a=0):

2R

2a

H2

11

233

, = 0.6 - 1(plus enclosed water)

413

A R H

RA R HH

=

+

20

Suction anchor Fully submerged, with ventilation, a > 0:

2R

2a

H

A2XH

KC =

21

Partly submerged, with ventilation Free air flow

Restricted airflow?

Suction anchor

2R

2a

H

33 0A

22

Templates with cover and mudmats.Range of experimental results

23

Protection cover made from tubular members. (approx 14 * 19m) (perforation ratio 0.27)

24

Computed and measured (forced oscillations) added mass. Protection cover

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5KC

C

a

Measured

Perforated plate

Sum of cylinders w/ interaction

2 AXKCB

=

25

Theoretical method. Horizontal circular disk

z R

a

z = d

z = h 3.

2.

1.

Disk

Circular disk, perforation ratio,

Restricted flow through disk

Pressure drop proportional to velocity squared.

Porous KC number:

2

1porKC KC

=

26

Estimated and measured damping including estimate on the effect of the edge vortex. Hatch 18 (perforation 0.25).

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

KCpor

C

b

Hatch 18

TotalMeasuredMeasuredMeasuredperforationEdge effect

27

Total force on hatch 18

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

KCpor

F

t

/

2

R

4

Hatch 18

28

Installation of gravity anchor. Use of method Molin & Nielsen(2004)

29

Model. Solid top, open top.

H = 3.42mR = 3.77m

30

Comparison with model tests. Suction anchor with central hole in top plate.

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Perforation ratio %

C

A

KC= 1.2KC= 1.2KC= 0.6KC= 0.6KC= 0.1KC= 0.1

A2XH

KC =

Red: MeasuredBlue: Computed

2R

2a

H

31

Added mass and linearized damping

332Rm

ACH

= 332RbBC

H=

( ) ( ) 12 2 22 33 331

2 2 2 22

Rb

tot A

a A

F A B X

C C X H

= + = +

32

Added mass and damping, fully submerged, 12.2% open area.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

KC = 2XA/H

A

3

3

/

(

R

2

H

)

Linearized A33, R=3.949 m, d/H=5.8548, R/H=1.156

T=8 sec

Asymptotic value: CA0 = 1.99

0 0.5 1 1.5 2 2.5 3 3.5 40.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

KC = 2XA/HB

3

3

/

(

R

2

H

)

Linearized B33, R=3.949 m, d/H=5.8548, R/H=1.156

T=8 sec

33

Added mass and damping, fully submerged, 12.2% open area.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

KC = 2XA/H

A

3

3

/

(

R

2

H

)


T=8 sec

Asymptotic value: CA0 = 1.99

0 0.5 1 1.5 2 2.5 3 3.5 40.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

KC = 2XA/HB

3

3

/

(

R

2

H

)


T=8 sec

34

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

KC = 2XA/H

A

3

3

/

(

R

2

H

)


T=8 sec

Effect of bottom proximity (1.0 and 0.25m from bottom)

0 0.5 1 1.5 2 2.5 3 3.5 40.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

KC = 2XA/H

B

3

3

/

(

R

2

H

)


T=8 sec

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

KC = 2XA/H

A

3

3

/

(

R

2

H

)


T=8 sec

0 0.5 1 1.5 2 2.5 3 3.5 40.2

0.4

0.6

0.8

1

1.2

1.4

1.6

KC = 2XA/H

B

3

3

/

(

R

2

H

)


T=8 sec

Added mass Damping

35

Effect of free surface proximity (2.5 and 1.25m from free surface)

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

KC = 2XA/H

A

3

3

/

(

R

2

H

)


T=5 secT=8 secT=12 sec

0 0.5 1 1.5 2 2.5 3 3.5 40.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

KC = 2XA/H

B

3

3

/

(

R

2

H

)



0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

KC = 2XA/H

A

3

3

/

(

R

2

H

)



0 0.5 1 1.5 2 2.5 3 3.5 40.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

KC = 2XA/H

B

3

3

/

(

R

2

H

)



Added mass Damping

36

Lift and drag force close to bottom (DNV RP C205)

37

Example: Intermediate phase of jacket installation

Four legs with mudmats, (circular plates).Platform stable before piling?

Fwave

38

Plate close to bottom

R: Radius of plate.h : Gap.V: Vertical velocity.

39

Added mass. Circular plate close to bottom

4 3

33

333

R 8 R 5 R hA log for 18 h h 3 2 R8 hA R for 13 R

= + =

40

Dynamic equation.

( ) ( )23333 B 3dA1m A V V F kh F g mg2 dh+ + + + = +

Inertia Slamming damping Spring External Netforce buoyancy

B D

B

1F C V V2

F BV

= =

Damping:

Quadratic:

Linear: Details:Nielsen 2007: Lecture notes in Marine operations, NTNU,

41

0 1 2 3 4 5 6 7 8 9 100

5x 106

R= 4 h0= 0.05

A

3

3

(

k

g

)

0 1 2 3 4 5 6 7 8 9 10

-4

-2

0

x 107

d

A

/

d

h

(

k

g

/

m

)

0 1 2 3 4 5 6 7 8 9 10-5

0

5x 107

t (sec)

F

(

N

)

Wave period 13.3sec, Fa = 22MNInitial clearance 0.05m

Lift force >0

0 1 2 3 4 5 6 7 8 9 10-2

0

2R= 4 h0= 0.05

V

(

m

/

s

e

c

)

0 1 2 3 4 5 6 7 8 9 100

5

10

h

(

m

)

0 1 2 3 4 5 6 7 8 9 10-2

-1

0

1

t (sec)

d

V

/

d

t

(

m

/

s

e

c

2

)

42

CFD is coming. Example ComFLOW. Courtesy: DNV /Tormod Be

Developed by University of Groningen, The Netherlands, in EU project SafeFlow(2001-04)

Based on Volume of Fluid method. Solves Navier Stokes equations for fluid and free surface.

Application areas: Wave in deck, slamming, green water, sloshing

Comflow is being further developed in project JIP Comflow-2 (2005-07) to account for

two-phase flow

arbitrary body motions

irregular wave inflow

Inflow boundary,Airy or Stokes5th wave

Structure

Fluid domain

43

Summary Proper added mass values crucial to find wave loads during installation. Water entry equations contain a slamming term. In splash zone: Added mass sensitive to submergence and frequency. By landing on bottom an increased added mass may contribute to softer landing. Coefficients very sensitive to inclination. The derivative of added mass versus distance from bottom pushes the object

upward.

Numerical and experimental tools available to find rough estimates on added mass and damping.

Viscous effects important. Theoretical expressions exist for several simple shapes. Real shapes very difficult to handle. CFD is being introduced. The future tool for load assessment

Still several pitfalls Requires very skilled users and proper codes.

How to estimate hydrodynamic coefficients applicable for lifting from the sea bed.Hydrodynamic coefficients for subsea structuresContentPhases of the installation processSubsea template Ormen LangeAdded mass for simple 2DformsNatural periods (Lightly damped) Added mass versus damping ?Added mass versus damping ?Added mass versus damping ?Water entry of TOGP template (2000)Water entry forces, calm waterWater entry forces, including wavesAdded mass for simple structures.Horizontal circular cylinder Close to bottomVertical force close to bottomA33 2D cylinder close to bottomCircular disc close to bottomPerforated plate, circular hollows, potential theorySuction anchorSuction anchorSuction anchorTemplates with cover and mudmats.Range of experimental resultsProtection cover made from tubular members. (approx 14 * 19m) (perforation ratio 0.27)Computed and measured (forced oscillations) added mass. Protection coverTheoretical method. Horizontal circular diskEstimated and measured damping including estimate on the effect of the edge vortex. Hatch 18 (perforation 0.25).Total force on hatch 18Installation of gravity anchor. Use of method Molin & Nielsen(2004)Model. Solid top, open top.Comparison with model tests. Suction anchor with central hole in top plate.Added mass and linearized dampingAdded mass and damping, fully submerged, 12.2% open area.Added mass and damping, fully submerged, 12.2% open area.Effect of bottom proximity (1.0 and 0.25m from bottom)Effect of free surface proximity (2.5 and 1.25m from free surface)Lift and drag force close to bottom (DNV RP C205)Example: Intermediate phase of jacket installationPlate close to bottomAdded mass. Circular plate close to bottomDynamic equation.Wave period 13.3sec, Fa = 22MNInitial clearance 0.05mCFD is coming. Example ComFLOW. Courtesy: DNV /Tormod BeSummary

how to estimate hydrodynamic coefficients applicable for lifting

Documents

x b x b x x

total force total force

mass contribution8added

kg5added mass

acceleration damping

damping crossing

water column5

linear damping force0