Subsea lifting operations

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1 Subsea lifting operations Hydrodynamic properties of subsea structures Finn Gunnar Nielsen Norsk Hydro O&E Research Centre 1

2 Hydrodynamic properties for subsea structures Content Forces on structures during crossing of the splash-zone. Landing on bottom Hydrodynamic phenomena. Hydrodynamic coefficients. Theoretical and experimental methods Actual values. Conclusions 2

3 Phases of the installation process 1) Lift-off from deck. 2) Lift in air 3) Crossing splash zone. 4) Lowering through the water column 5) Landing the structure

4 Natural periods Pendulum in air: T 1,2 = 2 π L g Pendulum in water: T = ml π α EA 3 2 E T T 1 = 2 2 = 2 T π π 3 = 2 π ( + ) m A L 11 mg ρ gv ( + ) m A L 22 mg ρ gv ( + ) m A33 L E α EA 4

5 5 Water entry of TOGP template (2000)

6 6 Water entry of TOGP template (2000)

7 7 Water exit of ROV

8 Water entry forces, calm water U z z z = 0 h x Vertical hydrodynamic force: da F = ρ gv + A U + U dh 33 2 h3 33 z z Hydrostatic Added mass Slamming V 8

9 Water entry forces, including waves z z = 0 h ζ V x Vertical hydrodynamic force: da Fh 3 = ρ gv + ρv ς + A 33 ς η + ς η dh + B ς η + ς η ς η ( ) B ( ) ( ) ( ) Slamming term Position dependent added mass 2 9

10 Interpretation of the terms 33 ρ gv ρvς ( ) da Fh 3 = ρ gv + ρv ς + A 33 ς η + ς η dh + B ς η + ς η ς η : Buoyancy force ( ) B ( ) ( ) ( ) : Froude Krilof force. Effect dynamic pressure in incident wave A ς η : Disturbance effect of body. Added mass times relative da 33 ( ) 2 acceleration. dh ς η : Slamming term, Effect of time dependent added mass. B ς η B ς η ς η : Linear and quadratic damping effect. 1 ( ) ( )

11 Water entry force, basis for derivation Ideal, non-viscous, non-compressible fluid Fast water entry Local fluid accelerations >>g. Added mass coefficient for infinite frequency No viscous effects Added as separate terms Body dimensions << wave length Solved as a perturbation to the incident wave field Similar expression valid for horizontal loads. 11

12 Water entry versus water exit Slamming term : Always upward force. Water exit: φ = 0 at free surface questionable. Slamming term neglected in most water exit implementations. Enclosed water / drainage very important during exit 12

13 13 Flow during water entry vs water exit. (Greenhow & Lin 1983)

14 Classical slamming solutions. 2R 2R Von Karman (1929) Wagner (1932) 1 1 F = ρc AU = ρc 2RLU 2 2 VonKarman : C = π 2 2 s s s z s z Wagner : C = 2π s s 14

15 Added mass for simple structures. Horizontal circular cylinder Added mass for horizontal 2D cylinder. 1 φ = 0 at z = φ=0 h η R 0.6 A 33 /ρπr Analytical expressions Asymptotic values Submergence h/r (da 33 /dh)ρπr De rivative of A 33 for horizontal 2D cylinde r. φ = 0 at z = 0 Numerical differentiation Asymptotic value Submergence, h/r

16 Added mass for simple structures. Sphere 2.5 Added mass for sphere, infinite frequency A 11 A A ii /ρr z c /R

17 Added mass for simple structures. Sphere 3.5 Adde d ma ss for sphe re, ze ro fre que ncy A 11 3 A A ii /ρr z c /R

18 Close to bottom No action from waves Modified slamming term Added mass for body close to fixed wall (Zero frequency limit) 18

19 Close to bottom F gv A 33 2 h3 = ρ 33η 0.5 η B η B ηη 1 2 da dh η 3 da 33 0 dh < 2R h 19

20 A 33 2D cylinder close to bottom 2.5 Added mass for horizontal 2D cylinder. dφ/dz = 0 a t z = 0 π 2 /3-1 2 A 33 /ρπr Centre distance from wall h/r 20

21 Circular disc close to bottom Far from bottom h/r >>1: Close to wall (Vinje 2001): 5 A 33 = 8 3 ρr WAMIT res ults for t/r=0.05 Asymptotic results for h/r<<1 Asymptotic results for h/r>> A 33 /ρr h/r

22 Perforated plate, circular hollows, potential theory Plate L*B= 15m*10m A33 = 0.625ρLB (0) 2 22

23 Suction anchor Fully submerged, no ventilation (a=0) A α, α = ρπr H (plus enclosed water) A = ρπ 2 R H 4 R 1+ 3 H H 2a 2R 23

24 Suction anchor Fully submerged, with ventilation 2a H 2R 24

25 Suction anchor 2a Partly submerged, with ventilation Free air flow A 33 0 Restricted airflow? H 2R 25

26 Subsea template w/protection grille Troll 26

27 27 Templates with cover and mudmats. Range of experimental results

28 Template. Numerical results. Sensitivity to period and draft. Heave Added Mass as a Function of Wave Period Added Mass [t] Wave Period [s] D = 3.5 m D = 4.0 m D = 4.5 m 28

29 Protection cover made from tubular members. (approx 14 * 19m) 29

30 30 Experimental determination of added mass and damping. Free oscillation tests Marintek

31 Computed and measured added mass Protection cover 1.2 Ca Measured Perforated plate Sum of cylinders w/ interaction KC 31 KC = X B 2 A π

32 Effect of pressure drop. Protection cover 1 τ Δ p= 2 ρ v v 2μτ τ : Porosity, open area/total area μ : Discharge coeff. ( 0.5-1) Added mass A_33/1000 (kg) Molin Measured Amplitude (m)

33 Protection cover linearized damping Linearized damping B1 (kns/m) Molin Measured Amplitude (m) 33

34 Effect of pressure drop. Sensitivity to discharge ratio 20 A_33 (kg) mju = 0.75 mju = 0.5 mju = KC 34

35 Conclusions 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. Numerical and experimental tools available to find added mass and damping. Viscous effects important. Depth dependent values difficult to establish. Theoretical expressions exist for several simple shapes. 35

Experimental determination of hydrodynamic coefficients

Experimental determination of hydrodynamic coefficients 1 Needs Analytical results for few geometries only Analytical damping: Linear (radiation only) Coefficients dependent of submergence Coefficients