6. SIMILITUDES Y DIFERENCIAS ENTRE LOS CUBISMOS DE PIERRE
6.3. Diferencias
For small subsea modules and tools, installation through the moonpool of the vessel is often preferred. This may reduce the dynamic forces, increase the limiting seastate and thus reduce the costs of installation and intervention operations. A typical application area is maintenance and repair operations of subsea production plants.
3.5.2 Simplified analysis of lift through moonpool
3.5.2.1 The simplified analysis described in this subsection is based on the following limiting assumptions,
— The moonpool dimensions are small compared to the breadth of the ship
— Only motion of the water and object in vertical direction is considered
— The blocking effect of the lifted object on the water in the moonpool is moderate
— Cursors prevent impact into the moonpool walls. Only ver-tical forces parallel to the moonpool axis are considered.
3.5.3 Equation of motion
3.5.3.1 A body object suspended inside a moonpool is consid-ered, see Figure 3-12. The moonpool may have varying cross-sectional area A(z). The draught of the ship is D. The vertical motion of the lifted body may differ from the vertical ship motion due to the winch operation and/or dynamic amplifica-tion in the hoisting system.
3.5.3.2 The equation of motion for the water plug can be writ-ten as
where
The ship heave motion is related to the sea surface elevation by a transfer function Gs (amplitude and phase),
The hydrodynamic pressure force acting on the water plug can also be related to the sea surface elevation by a transfer func-tion Gw (amplitude and phase),
3.5.3.3 Both Gs and Gw can be found by integrating the pres-sure p obtained by a sink-source diffraction program over the cross-section of the moonpool at z = -D. Gs and Gw are func-tions of wave frequency and wave direction.
Figure 3-12
Suspended body in a moonpool.
Μ = mass of water plug [kg]
Α33 = added mass of water plug (see 3.5.4.3) [kg]
ζ = motion of water plug [m]
ζs = heave motion of the ship [m]
ζb = motion of body in moonpool [m]
ζw = sea surface elevation outside moonpool [m]
Cs = damping coefficient for relative motion between water plug and ship [kg/m]
Cb = damping coefficient for relative motion between water plug and body [kg/m]
K = ρgA water plane stiffness [kg/s2] F(t) = wave excitation force on water plug [N]
( )
( )
())
( 33
t F K C
C A
M
b b
b
s s s
= +
−
− +
−
− + +
ζ ζ ζ ζ ζ
ζ ζ ζ ζ ζ
&
&
&
&
&
&
&
&
&&
w s
s
G ζ
ζ =
[m]w
G
wt
F ( ) = ζ
[N]p
ζw
ζ ζb
ζs
A(z)
D
z
3.5.4 Resonance period
3.5.4.1 The natural period of vertical oscillations of the water plug and the damping conditions given by the moonpool design are important for the dynamic forces on an object inside the moonpool.
3.5.4.2 In general the cross-sectional area of the moonpool is a function of the vertical position z. Assuming the moonpool walls do not move, the requirement of continuity yields
3.5.4.3 The requirement of energy conservation gives,
where
and
3.5.4.4 A33 is the added mass for vertical oscillation of the water plug, which can be expressed as
3.5.4.5 The parameter κ has been found to be within 0.45 and 0.47 for rectangular moonpools with aspect ratios between 0.4 and 1.0. Thus κ = 0.46 can be used for all realistic rectangular moonpools. For a circular moonpool κ = 0.48.
3.5.4.6 The resonance period is found from the energy conser-vation expression,
or
3.5.4.7 The energy-equivalent mass (mass plus added mass) moving with the surface velocity is;
3.5.4.8 If the moonpool has a constant cross-sectional area A(z) = A, the above expressions simplify to the following;
3.5.5 Damping of water motion in moonpool
3.5.5.1 The amplitude of the water motion in the moonpool, in particular for wave excitation close to the resonance period T0, depends on the level of damping. In addition to inviscid damp-ing due to wave generation, dampdamp-ing is provided by viscous drag damping caused by various structures like guidance struc-tures, fittings, cofferdam or a bottom plate.
3.5.5.2 In model tests of several offshore diving support ves-sels and work vesves-sels with different damping devices, the water motion inside a moonpool has been investigated. In these tests the relative motion between the water plug and the ship at the moonpool centre axis has been measured. An ampli-tude RAO for the relative motion is defined as;
where
3.5.5.3 Figure 3-13 shows the measured RAO for different structures causing damping of water motion in moonpool.
Figure 3-13
Measured relative water elevation in a moonpool per unit incom-ing wave amplitude. (Courtesy of Marintek)
3.5.5.4 The water plug is excited both by the incoming waves and by the vertical ship motion. Hence it is not straightforward to derive damping data directly from such curves. An approx-imated approach has been used in order to estimate the damp-ing given by the various dampdamp-ing arrangements. An approximate linearised complex equation of motion of the water plug in an empty moonpool (without a lifted object) is;
)
ζw = sea surface elevation outside moonpool [m]
w
Relative water elevation in moonpool
0
Naked moonpool Minor fittings
Guidance structure Cofferdam
Guid.+ 50% bottom plate
( ) ( )
where
3.5.5.5 The ratio between the motion of the water plug and the sea surface elevation outside the moonpool is;
3.5.5.6 To obtain a relationship between transfer functions Gw and Gs, some simplifying assumptions are made,
— The moonpool dimensions are small compared to the ship breadth
— Excitation force due to incoming waves, F1, and due to ship motion, F2, can be assessed as for a ship without moonpool
— The fluid pressure expressions valid for long waves can be
— Deep water is assumed.used
The following approximate expressions for the excitation force can then be used;
where
PFK = the undisturbed (Froude-Krylov) dynamic fluid pres-sure [N/m2]
A33 = the added mass of the water plug as given in 3.5.4.4 [kg]
Hence,
where k = ω2 / g.
3.5.5.7 The amplitude ratio of relative water plug elevation to incoming wave elevation is then given by
3.5.5.8 In Figure 3-14 an example case of the relative water elevation inside the moonpool is plotted. The motion transfer functions of a typical 80 m long diving support vessel have been used. Gs for vertical moonpool motion has been inserted in the above expressions, and the RAO curves have been com-puted for varying relative damping, η.
3.5.5.9 The results are uncertain for the shortest wave periods (T/T0 < 0.8), where the curve shapes differ from the model test results.
3.5.5.10 The maximum RAO values, found at resonance, are shown as a function of the relative damping, for the cases with-out bottom plate, in Figures 3-14 and 3-15.
Figure 3-14
Calculated relative water elevation, no bottom plate (β = 1).
Figure 3-15
Calculated relative water elevation at resonance.
3.5.5.11 Approximate relative damping values for the cases without bottom plate have been found by a comparison between Figure 3-13 and Figure 3-14. The following approxi-mate relative damping values have been assessed,
3.5.5.12 The quadratic damping coefficient Cs can be esti-mated from the relative damping and the motion. The follow-ing approximation may be used,
where ζ0 is the amplitude of relative motion.
M = = total mass of water plug, including added mass [kg]
K = ρgA = water plane stiffness [kg/s2] Cs1 = = linearised damping [kg/s]
η = damping ratio (relative to critical damping) [-]
Gs = transfer function for vertical moonpool motion [m/m]
Gw = transfer function from wave elevation to excitation force [N/m]
Relative water elevation inside moonpool
0
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 T / T0
Elevation / wave amplitude
0.03
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Relative damping
Max. relative elevation / Wave amplitude
KM
3.5.6 Force coefficients in moonpool
3.5.6.1 Restricted flow around the object inside a moonpool leads to increased hydrodynamic forces. Increased drag coeffi-cient CD and added mass coefficient CA to be used in the cal-culation can be taken as
where
For Ab/A > 0.8 a more comprehensive calculation method should be used.
3.5.6.2 The dynamic behaviour of the lifted object when leav-ing the lower moonpool end durleav-ing lowerleav-ing or prior to entry at lifting, should be analysed by a time domain calculation method, in irregular waves.
3.5.6.3 For an object close to the lower end of the moonpool, a conservative approach is to analyse the dynamics, using hydrodynamic forces based on the wave kinematics of undis-turbed waves and hydrodynamic coefficients for unrestricted flow condition.
3.5.6.4 Realistic impact forces between lifted body and moon-pool walls require accurate stiffness data for the cursor system.
3.5.7 Comprehensive calculation method
A more comprehensive calculation method should be used, either if the solid projected area covers more than 80% of the moonpool section area, or if the vertical motion of the lifted object differs from the vertical motion of the vessel at moon-pool, i.e.:
— if a motion control system is applied when the lifted object is inside the moonpool, or
— if the object is suspended in soft spring, such as a pneu-matic cylinder.
3.5.7.1 The following calculation steps are defined,
1) Calculate the first order wave pressure transfer functions at the moonpool mouth, using a diffraction theory program with a panel model of the ship with moonpool. Emphasis should be put on obtaining numerical stability for the moonpool oscillation mode.
2) Carry out a non-linear time domain analysis of the system, with a model as described below. The analysis should be made for relevant irregular wave sea states. Calculate motion of the lifted object and forces in lifting gear.
3.5.7.2 The following analysis model is proposed,
a) The lifted object is modelled, with mass and hydrody-namic mass and damping.
b) The lifting system is modelled, with motion compensator or soft spring, if applicable.
c) The water plug inside the moonpool is modelled as a fluid body moving only in vertical direction, with mass equal to the energy-equivalent mass given in 3.5.4.7.
d) The water body should be excited by the water pressure multiplied by the section area of the moonpool opening.
e) The interaction between the water plug and the moonpool walls should be modelled a quadratic damping coupling in vertical direction.
f) The interaction force between the water plug and the lifted object is found as:
where
vr = relative velocity between lifted object and water plug [m/s]
Ab = solid projected area of the lifted object [m2] V = volume of lifted body [m3]
A33 = added mass of lifted body [kg]
= vertical acceleration of the water plug [m/s2] = vertical acceleration of lifted object [m/s2]
3.5.7.3 The use of Computational Fluid Dynamics (CFD) may not be recommended for moonpool dynamics. Even though CFD can analyse the fluid dynamic interaction between the lifted object and the water plug inside the moonpool, it is dif-ficult to couple with the dynamic characteristics of ship in waves and the response of the lifting system. Force predictions may hence be uncertain.
3.6 Stability of lifting operations