OMAE2007-29244

1 Copyright © 2007 by ASME

Proceedings of OMAE2007 26th International Conference on Offshore Mechanics and Arctic Engineering

June 10-15, 2007, San-Diego, USA

OMAE2007-29244

INVESTIGATION INTO THE SENSITIVITY OF THE DYNAMIC HOOK LOAD DURING SUBSEA DEPLOYMENT OF A SUCTION CAN

J. Ireland Subsea7

PO Box 205, Eldfiskvegen 1, N-4056 Tananger,

Norway

G. Macfarlane Australian Maritime College PO Box 986 Launceston,

Tasmania, 7250 Australia

Y. Drobyshevski INTEC Engineering Pty Ltd

190 St Georges Terrace, Perth, Western Australia 6000

Australia

ABSTRACT

Suction cans are commonly used as foundations of fixed offshore structures, subsea equipment, and anchors of mooring lines. During the offshore installation phase, when a suction can is submerged, it attracts large heave added mass, which may be an order of magnitude higher than the mass of the can in air. Due to motions of an installation vessel the dynamic hook load may significantly exceed the submerged weight of the can. The dynamic hook load must be accurately predicted, as it governs selection of the vessel, lifting gear and rigging, and defines the allowable installation sea state.

The objective of this paper is to examine the sensitivity of the dynamic hook load to hydrodynamic properties of the suction can, in particular its heave added mass and damping. This research is motivated by the lack of data on such properties, which are usually estimated by simplified methods with some engineering judgement and assumptions. A single degree of freedom system is considered and the frequency domain spectral analysis is used, which employs the stochastic linearization of the nonlinear damping component.

The added mass and damping of a 6-meter diameter suction can of dimensions typical for Australian North West Shelf developments have been determined by testing a 1:10 model in the 4.1 m deep basin of the Australian Maritime College. Free decay tests were conducted at several frequencies and the added mass, linear and nonlinear damping components determined. The effect of open hatches on the hydrodynamic properties was examined by fitting the model with hatches of various diameters, with up to 4.8% of the relative area open. Results of the tests demonstrate that the added mass and damping are higher, when compared with estimates based on

empirical data for non-oscillatory flow. Within the Keulegan-Carpenter number range of 0.1 – 1.0, open hatches impact significantly on the added mass and produce additional damping, which is found to be linear with the heave velocity. Results of the tests and their interpretation are discussed.

Sensitivity analysis shows that if the model test results are used in the dynamic lift analysis for an installation vessel and sea states considered, the predicted hook load is generally less than its values obtained by using simplified estimates. In particular, the increase in linear damping due to open hatches is responsible for up to 20% reduction in the dynamic hook load, with 2.4% of the relative top area open.

1. INTRODUCTION Offshore operations often require deployment and recovery

of heavy objects (structures, subsea packages, anchors, etc.) to or from the seabed. The analysis of lifting operations in these conditions usually aims at prediction of the maximum hook loads, so that the installation vessel and the lift equipment can be selected and the lift rigging designed. Due to wave induced motions of an installation vessel, hydrodynamic forces on the object and flexibility of the lift rigging the dynamic hook load may significantly exceed the weight of the object. In deep water conditions, as the stiffness of the rigging reduces and its weight increases, the system may be prone to adverse dynamic amplification, as the natural period of a suspended structure may fall in the range of predominant wave periods, which excite the installation vessel.

Prediction of the dynamic hook loads and related issues have been addressed in several design codes, for example DNV


(1996, 2000), and in a number of studies, which point to the importance of the hydrodynamic properties of the object. For example, Oritsland and Lehn (1987) presented findings from the experimental study on added mass and drag coefficients of several generic structures during subsea lowing. Niedzwecki and Thampi (1991) examined the occurrence of snap loads in cable systems, and concluded that the use of idealized models to predict the hydrodynamic added mass of a subsea package was not entirely a satisfactory approach. Rowe, et al (2001) indicates that the shape of the item to be installed, which determines its added mass, is crucial to the dynamic response of the package, and to the ability to install it.

An important example of such a situation, referred to by Rowe, et al (2001) and Frazer, et al (2005), is a suction can (pile, caisson). Suction structures are commonly used as foundations of fixed offshore structures, subsea equipment, and mooring anchors. When the suction can is suspended off the crane and submerged, it attracts large heave added mass, which, due to its special shape, may be an order of magnitude higher than mass of the structure in air. Therefore, the dynamic hook load may reach unexpectedly high values.

Dynamic loads of large amplitude may result in snap loading on the wire or dictate the increased capacity of lifting equipment, or a different vessel. In Australian conditions, such an option is rarely attractive due to high mobilization costs of heavy lift vessels, many of which are based in South East Asia. Active or passive heave compensators may need to be used, which add to project costs. The same applies to passive compensators in the form of synthetic slings (“stretchers”), which are to be sized to higher safety factors than wire slings, and tend to be long and inefficient. Long period South Westerly swell, a persistent feature of the Australian North West Shelf, also makes selection of the passive heave compensator difficult.

The above circumstances place special emphasis on the accuracy of the installation analysis, which provides background information for key project decisions, and which in turn depends on the level of knowledge of the hydrodynamic properties. A review conducted by the authors indicates that, in spite of common use of suction cans, there is little information in open literature on hydrodynamic coefficients of such structures, which would reflect their real shapes and dimensions. An interesting study described by Morrison and Cermelli (2003) for a suction pile model (6“ in diameter and 30” long) identified that openings in the top plate can impact significantly on the heave added mass and increase the hydrodynamic damping. For the subsea lift analysis, however, it is a common practice to estimate the added mass and drag coefficients using data on generic bodies from design codes and textbooks with some simplifying assumptions. The objective of this paper is to examine how the availability (or accuracy) of such information may impact on the predicted hook loads.

The material is set out as follows. In Section 2, a methodology of the dynamic lift analysis is described, which employs the single degree of freedom model and follows the frequency domain approach. Stochastic linearization of the nonlinear damping is used, a common method for linearizing viscous drag forces in the spectral analysis of offshore structures (Brebbia and Walker, 1979). In Section 3, the hydrodynamic coefficients of a 6-meter diameter suction can are estimated from empirical data, and also determined by conducting free decay tests with a 1:10 model. Heave added

mass, linear and quadratic damping coefficients were determined for several frequencies, and the effect of open hatches in the top plate was investigated. In Section 4, these hydrodynamic coefficients are used in the sensitivity analysis, which shows significant impact of the open hatches on the dynamic hook loads, and demonstrates that hydrodynamic properties obtained by the model tests produce less onerous results. Concluding remarks and recommendations are given in Section 5

2. ANALYSIS METHODOLOGY The dynamic system considered involves a subsea

structure (suction can), which is suspended on the crane wire from an installation vessel. The purpose of the analysis is to determine dynamic tension in the wire due to wave induced motions of the vessel. It is assumed that the structure is submerged well below the free surface and above the sea bed, so that the effects of the free surface and the sea bed proximity can be neglected. Due to motions of the vessel the tip of the crane moves in surge, sway, and heave. Heave motions play the dominant role in the wire tension, while surge and sway produce pendulum-type oscillations of the structure. For the axis-symmetric body, such as suction can, coupling between heave and other motions is negligible, so that surge and sway of the crane will have minor effect on the wire tension. Therefore, in the following analysis the attention is focused on heave motions, and the resulting dynamic tension in the lift rigging.

The analysis can be conducted in the frequency or time domain. Time domain simulations are widely used nowadays, in particular for complex marine operations. For a simple single degree of freedom system frequency domain analysis is preferred owing to its simplicity and ease of interpretation; the analysis algorithm is outlined below.

Let us assume that in regular waves, heave motions of the

crane tip )(txh and that of the structure )(tx can be expressed in the form:

txx hh ωcos0= ; )cos(0 αω −= txx (1)

Here ω denotes the circular frequency and α is the phase

shift between the two motions. Assuming that within the expected range of motions the lift rigging has constant stiffness K , the dynamic tension in the rigging can be obtained as:

[ ]ttxKxxxKT hhD ωαωω cos)cos()()( 0 −−⋅=−= ;

( ) ( )22

0

sin)(1cos)( αωαω xxKxT

Th

DD +−⋅== . (2)

Here 00 /)( hxxx =ω - is the response amplitude operator

(RAO) of the structure heave, and DT denotes the RAO of tension in the lift rigging.

In the simplest case of an axis-symmetrical structure, its heave response is decoupled from other motions; it can be described by single equation:


tKxKxxFxM hD ωcos)( 0=++⋅ &&& . (3)

Here the total mass of the system AmmM += comprises the structural mass in air m (including mass of the lift rigging) and the hydrodynamic added mass Am . The damping force

DF is usually expressed in the form:

...)( 3321 +++= xBxxBxBxFD &&&&& . (4)

Here coefficients iB are assumed to be independent of the motion velocity. Introducing coefficients iβ and the natural frequency nω , the equation of motion (3) can be re-written as:

txxxxxxx hnn ωωωβββ cos... 0

223321 =+++++ &&&&&& (5)

MBi

i =β ; MK

n =ω (6)

To obtain a solution of (5) in the frequency domain, the

damping force is usually linearised by replacing (4) with:

( )xMF ED &β≈ (7)

A common method for obtaining the damping coefficient Eβ is to equate the work done by the nonlinear (quadratic) and the linearised damping forces (Timoshenko, 1954). An equivalent method, presented for example by Krylov (1932) with further reference to Newton, assumes that the damping is relatively weak, i.e. coefficients kβ are small, and leads to the following general expansion:

( ) ( )≈+⋅⋅⋅= ∑ − 210

4k

k

kkkE OxN βωβ

πβ

( ) ...43

38 2

03021 +++≈ xx ωβωβπ

β (8)

Here the sum is taken over all terms in (4) and members of the higher order in kβ are neglected. Coefficients kN are given by the following formula:

( )∫ −=1

0

2/21 dttN kk ;

...4,3,2,1;...158;

163;

32;

4== kN k

ππ (9)

Equations (8) and (9) enable representation of the damping

force (4) involving any powers of the velocity by the equivalent linear damping force. Most frequently only two terms (linear and quadratic) in (8) are used; in studies on viscous roll damping, for example (Himeno, 1981), three terms in equation (8) were retained.

Once the equation of motion (3) has been linearised, its solution is given by the known formulae (Timoshenko, 1954):

( ) ( )222 21

1)(ωβω

ω⋅+−

=x ;

212tan

ωωβα

−⋅

= ; nωωω /= (10)

Here the ratio β expresses the damping coefficient EB as a percentage of the critical damping:

n

EE

KMB

ωβ

β22

== . (11)

As the amplitude of motion 0x is unknown, equations (8)

and (10) are solved by iterations, with the new damping coefficient Eβ computed at each iteration step after the amplitude 0x at the previous step has been determined.

The extension of the above approach to irregular sea state

is possible by using spectrums of waves and responses. For a given sea state spectrum )(ωwS , the heave motion spectrum at the crane tip ( )ωhS is determined from the heave RAO ( )ωhx :

( ) ( ) ( )[ ]2ωωω hWh xSS ⋅= (12)

If the structure RAO ( )ωx is known from (10), spectrums

of the structure response and the dynamic tension can be computed:

( ) ( ) ( )[ ]2ωωω xSS hS ⋅= ; ( ) ( ) ( )[ ]2ωωω DhF TSS ⋅= (13)

The equivalent damping coefficient involved in (10), (11)

is unknown at this stage and must be found by iterations. Linearization formula (8) is now replaced with a more general approach known as the stochastic linearization, which is based on minimizing the variance between the nonlinear and the equivalent linearised damping forces over the spectrum (Brebbia and Walker, 1979). If only the first and second order terms in velocity are included in (4), it leads to:

VE σβπ

ββ ⋅+= 218

. (14)

Here Vσ denotes the standard deviation of the heave velocity, computed from the velocity spectrum:

( )2/1

0

2 ⎟⎠

⎞⎜⎝

⎛ ⋅= ∫∞

ωωωσ dS SV (15)


The equivalent damping coefficient (14) should be substituted back in (13) and iterations repeated until its value stabilizes. Then, the spectrum of the heave motion and dynamic tension (16) can be computed. This enables the stochastic responses to be predicted, including significant and maximum motions and tensions over given exposure time. Finally, the submerged weight of the structure is added to the dynamic tension, to produce the total maximum tension in the lift rigging (hook load).

3. HYDRODYNAMIC PROPERTIES OF SUCTION CAN

Structure Details Particulars of the suction can used in this study are given in

Table 1. Selected dimensions are typical for suction cans used as foundations of subsea manifolds in oil and gas developments in Australia’s North West Shelf. Figure 1 shows geometry and dimensions of the model made to scale 1:10. The model was fabricated out of rolled 2mm steel plate. A photograph of the model is shown in Figure 2.

Table 1: Details of the suction can

Description Full scale Model Units

Diameter D 6.000 0.600 m

Height H 6.000 0.600 m

Top plate area S 28.27 0.2827 m

Hatch pair # 1diameter d 0.380 0.038 m

area SH 0.113 0.00113 m2

Hatch pair #2 diameter d 0.537 0.054 m

area SH 0.226 0.00226 m2

Hatch pair #3 diameter d 0.658 0.066 m

area SH 0.340 0.00340 m2

Height of coaming -- 0.500 0.050 m

Wall thickness -- 0.020 0.002 m

Water density ρ 1025 1000 kg/m3

Usually, suction cans are fitted with one or two hatches in the top plate, which can be left open during the descent to vent out air and water and closed by a remotely operated vehicle before the suction operation commences. To investigate the effect of open hatches on the hydrodynamic properties, three pairs of hatches were installed in the top plate with 50 mm high coaming; all hatches were fitted with polyethylene plugs. Each of the three pairs of hatches provided the relative open area HS of 0.8%, 1.6% and 2.4%.

Estimated Hydrodynamic Properties For the purpose of the sensitivity analysis, hydrodynamic

properties of the suction can (full scale) were initially estimated

using empirical data on similar bodies available in literature. Table 2 presents results of such estimations, which utilized the following data and assumptions:

TRUE 600,00

TRUE R300,00

Figure 1 Layout of the suction can

Figure 2 General view of the model


• Unbounded fluid flow and infinite water depth are

assumed. • Hydrodynamic added mass is calculated as mass of the

entrapped water inside the can plus 50% of added mass of a circular flat disk, to account for the added mass attracted by the top plate.

• Pressure drag is assumed to be the equivalent to that of a hollow hemisphere in steady flow, for which Hoerner’s (1965) data is available. Formulation of Tao et al. (2000) for the viscous damping of a half-submerged vertical cylinder in heave has been also used and found to produce a similar value.

• Friction drag on the outside surface is estimated using data in Hoerner (1965); it is found to be small and incorporated into the total quadratic drag.

• The effect of open hatches has not been included on the assumption of their small size and because no method is readily available.

Table 2: Estimated hydrodynamic properties in heave

Description Notation Full scale Units

Added mass mA 211.0 tonne

Added mass coefficient CA 1.21 -

Pressure drag area S 28.3 m2

Pressure drag coefficient CD 1.42 -

Friction drag area 2π RH 113.1 m2

Friction drag coefficient Cf 0.007 -

Total drag reference area S 28.3 m2

Total drag coefficient CD 1.45 -

Model Test Program

In order to determine the hydrodynamic coefficients more accurately, model tests were conducted in a deep water basin at the Australian Maritime College; details of the testing facility are given in Table 3. The model was suspended in the middle of the tank depth, so that the distance between the top plate (or bottom) of the model and the water surface (or the tank floor) was 1.75 m, or 2.92 the model height. The distance of the model vertical axis from the nearest wall was 2.6 m, or 4.33 the model diameter. It is estimated that such clearances make boundary effects negligible, and the hydrodynamic properties should not be appreciably affected by the free surface.

Table 3: Dimensions of testing facility

Dimension Magnitude

Length 25 metres

Width 12.5 metres

Water Depth 4.13 metres

The model test program (Table 4) included free decay tests at several frequencies of oscillations to cover the range of periods 5.0 – 10.0 s in full scale, usually associated with ship motions. This was achieved by incorporating springs of different stiffness into the suspensions system (above water), so that heave oscillations at 5 frequencies could be generated. The springs were made of stainless steel and calibrated to confirm their linear behaviour within the target range of deflections.

Table 4: Summary of model test program

Description Parameter

Spring Stiffness 3407.3 N/m

2329.8 N/m

1641.6 N/m

1227.6 N/m

824.3 N/m

Initial Displacements 90 mm, 60 mm, 30 mm

Hatch Conditions All hatches closed

Pair of hatches #1 (small) open

Pair of hatches #2 (medium) open

Pair of hatches #3 (large) open

All hatches open

The initial downward offset of the model was generated

with a special pulley system with an electro-magnetic release; offsets of 30 mm, 60 mm, and 90 mm were tested for comparison. Heave motions of the model were measured by a linear transducer; a wave probe was also installed in the tank to check amplitudes of radiated free surface waves. Throughout the tests no radiated waves were detected; the wave motion in the tank was found to remain at its usual background level. This confirmed the expectation of negligible free surface effects due to relatively large submergence of the model. Therefore, the effect of wave reflection in the tank was considered to be negligible, and no special measures were taken. Photographs of the test rig can be seen in Figures 3 and 4.

When the model was oscillating in heave, no sway (pendulum), roll or yaw motions were observed, although the model was free to move in these degrees of freedom. In total, 46 tests were run; several tests were repeated to confirm consistency of results.

Test records have been post-processed to determine the added mass, linear and nonlinear (quadratic) damping components. The added mass is determined from the natural frequency of un-damped motions; the added mass coefficient is defined as:

HRmC A

A 2ρπ= (16)

The two damping components were obtained by fitting a

straight line to the decrement curve, which is proportional to the equivalent damping (8):


Figure 3 Model test set up

Figure 4 Suction can model with hatches # 3 open

=≈−

Ecba β

ωπ2

cHHcOcNN 212

2211

1 )(22 +≈++= − βωβ ; (17) Here a, b, and c denote absolute heave displacements at peaks, troughs, and the average, respectively, in the motions time history. Typical heave time history and the decrement curve are shown in Figures 5 and 6. After coefficients of the linear approximation are found, the damping coefficients can be calculated from the equations:

ωπβ211 =H ; 22 3

4 β=H (18)

The two damping components have been presented in the non-dimensional form:

ωβ

ω 2211

1 ==MBB ; (19)

DCSM

S

BB ===

ρβ

ρ

222

2

21

; (20)

Here the second (quadratic) term is identical to usual drag coefficient. The total equivalent damping links the two components by the following equation:

KCM

SRBBM

cSBBB EE ⋅+=+== 22121 3

223

821

2 πρ

ωω

πρ

ωβ

(21)

where the Keulegan-Carpenter number is:

RcKC /π= (22)

-40

-30

-20

-10

0

10

20

30

40

0 20 40 60 80 100

Time (sec)

Heave X (mm)

Troughs Peaks Heave Time History Figure 5 Typical heave time history


0.00

0.05

0.10

0.15

0.20

0.25

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Average amplitude c (m)

Decrement (a-b)/c

Figure 6 Typical extinction curve and linear approximation

Results of Model Tests Heave added mass is found to be stable and almost

independent of frequency of oscillations for all hatch conditions. In conditions with open hatches some reduction in the added mass was observed with decreasing amplitude (KC number). As the size of open hatches increases, the added mass reduces significantly, much faster than one would anticipate from proportional reduction of the impermeable top area; refer to Figure 8 and Table 5. When all three groups of hatches were open, this corresponded to 4.8% of the top area open, the added mass reduced by more than 30%. Compared with empirical estimates (Table 2), the added mass in “all hatches closed” condition found in the tests is higher by about 25%.

Another phenomenon observed in the tests was rapid increase in the linear damping with increasing size of open hatches, along with gradual reduction in the quadratic damping component; this can be observed in Figure 9 and Figure 10. In “all hatches closed” condition, the linear damping is generally small, being dominated by the quadratic (drag) component. As the size of the open hatches increases this situation slowly reverses, the linear damping becomes more pronounced, and in “all hatches open” condition its contribution is clearly dominant. The drag coefficient, on the contrary, reduces from the average value of about 3.6 in “all hatches closed” to about 2.0 in “all hatches open” condition.

To interpret the change in damping caused by the open hatches, especially the significant increase in the linear damping, it is worth noting that the range of KC number for the flow through the hatch is estimated to be KC = 1.0 - 10.0 based on the orifice diameter, while the corresponding KC number for the suction can itself is KC = 0.1 – 1.0. The pressure gradient exerted on the portion of the top plate around the orifice may vary significantly due to large changes in the “local” KC number. For example, it is evident from results reported by De Bernardinis et al. (1981) that the “drag coefficient” which expresses the pressure drop in the oscillating flow through an orifice increases rapidly with reduction in KC number.

A similar situation in external flows (or bodies in oscillatory motion) has been investigated by many researches (for example, Bearman et al (1985), Venugopal et al (2006)). To describe this trend in CD, Huse (1987), Huse et al. (1990),

and Garrison (1990) proposed the “wake flow model”, which accounts approximately for the effect of the body moving through its own wake, and confirms in particular that the drag coefficient CD becomes inversely proportional to KC number.

If a similar “wake flow” dependence CD (KC) is assumed for the flow through an orifice, it leads to the following formula for the linear damping of the suction can with open hatches:

HHC SM

SRBBB ⋅+= 211 32πρ

. (24)

Here CB1 is the linear damping coefficient in “all hatches

closed” condition, M is the total mass as in (3), and HB is a special factor to account for the effect of hatches. This factor is found to be relatively stable with an average value of about 100; it reduces slowly when the relative open hatch area increases in the range %8.4%.....8.0=HS ; refer to Figure 7.

It is also found by the tests that the quadratic drag coefficient (with all hatches closed) is significantly higher than the estimation based on the steady flow with the error exceeding 100%; it also exceeds the prediction for the heaving half-submerged cylinder based on formulation of Tao et al (2000).

As the size of open hatches increases, more fluid is allowed to pass through the hatches, rather than around the outer edge of the top plate. As a result, fluid velocities at the outer edge reduce, which may explain the reduction in the quadratic damping, evident in Figure 10.

Table 5: Effect of open hatches on heave added mass

Percentage of Top Area Open

Added Mass Coefficient

Reduction in Added Mass

0.00% 1.53 0.00%

0.80% 1.48 - 9.7%

1.60% 1.40 - 8.4%

2.40% 1.33 - 13.1%

4.80% 1.06 - 30.6%

0

20

40

60

80

100

120

0.0% 1.0% 2.0% 3.0% 4.0% 5.0%Percentage of Top Area Open

BH bar _

Figure 7 Hatch damping factor in equation (24)


0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

0.0% 1.0% 2.0% 3.0% 4.0% 5.0%Percentage of Top Area Open (%)

CA

No Hatches Open

Hatches #1 Open

Hatches #2 Open

Hatches #3 Open

All Hatches Open

Average Ca

Figure 8 Added mass coefficient vs Percentage of hatch area open

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16


B1(bar)

No Hatches Open

Hatches #1 Open

Hatches #2 Open

Hatches #3 Open

All Hatches Open

Average

Figure 9 Linear damping vs Percentage of hatch area open

0.0

1.0

2.0

3.0

4.0

5.0


B2(bar)

No Hatches Open

Hatches #1 Open

Hatches #2 Open

Hatches #3 Open

All Hatches Open

Average

Figure 10 Quadratic damping vs Percentage of hatch area open


4. SENSITIVITY OF THE DYNAMIC HOOK LOAD Results of the model tests have been used to carry out

several sensitivity studies, to determine the impact of the hydrodynamic coefficients on the hook loads during the deployment or recovery of the suction can.

Stiffness properties of a typical rigging system are given in Table 6; dynamic system properties, which are based on the model tests, are given in Table 8. Heave natural period of the suction can varies within 7.3. – 7.5 s, depending on the size of open hatches, compared to 6.8 s, which follows from the estimations.

Table 6: Stiffness properties of the rigging

Description Parameter

Wire length 750 m

Spring constant 150,000 kN

Rigging stiffness 200 kN/ m

Static tension (submerged weight) 250 kN

The analysis utilized motion RAOs of a typical installation

vessel, from which motions at the lifting winch were predicted. The spectrum of the dynamic hook load was calculated for two sea states, presented in Table 7, both with the significant wave height of Hs =2.0 m.

Table 7: Sea states

Description Sea state “A” Sea state “B”

Sea spectrum JONSWAP JONSWAP

Significant wave height 2.0 m 2.0 m

Peak period 7.0 s 12.0 s

Peakedness parameter 1.00 3.00

Results of the analysis are summarized in Table 9 and

Table 10. Heave RAOs of the suction can for various hatch conditions are given in Figures 11 and 12.

First of all, it can be seen that open hatches impact significantly on the dynamic hook load, as could be expected from the differences in hydrodynamic properties. For the percentage of hatch area considered in this study (from 0.8% to 2.4%), the effect of open hatches reduces the dynamic hook load up to 20% compared with “all hatches closed” condition. The corresponding reduction in the maximum heave RAO is as large as 40% for the largest pair of hatches with 2.4% of open area.

Secondly, it is evident that by using accurate hydrodynamic properties, rather than empirical estimations, less onerous hook loads are predicted. In terms of the total maximum hook load (dynamic + submerged weight), the difference ranges from 22% to 29%, depending on the size of the hatches. For the dynamic component alone, the tension

amplitude is reduced by 36% to 47%. Even in “all hatches closed” condition, using hydrodynamic coefficients obtained by model tests reduces the peak of heave RAO by about 35% in short period sea, and up to 60% in the long period sea, compared with the RAO based on estimations.

Finally, it can be seen that changes in the dynamic wire tension are somewhat more pronounced in the short period sea, because of its peak period being closer to the natural heave period of the system. This situation may change, however, if different type vessel is used, which may have different motion characteristics.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

Omega, 1/s

X, m/m

Estimations No hatches Hatch 1 Hatch 2 Hatch 3

Figure 11: Suction can heave RAO. Sea state “A”

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20Omega, 1/s

X, m/m

Estimations No hatches Hatch 1 Hatch 2 Hatch 3

Figure 12: Suction can heave RAO. Sea state “B”


Table 8: Properties of the system

Case

Added mass coefficient

AC

Total Mass

M , t

Natural frequency

nω , 1/s

Linear damping

1B

Quadratic damping

DCB =2

Estimations 1.21 236.0 0.921 0.000 1.45

Hatches closed 1.51 288.0 0.833 0.010 3.60

Hatches # 1 open 1.48 282.0 0.842 0.030 3.12

Hatches # 2 open 1.40 268.5 0.863 0.051 2.71

Hatches # 3 open 1.33 256.0 0.884 0.067 2.43

Table 9: Dynamic hook load: Sea state “A”

Model testsDYNAMIC HOOK LOAD Estimations Hatches

closed # 1 # 2 # 3Significant Tension TSIG = 2*RMS kN 218.1 139.9 133.1 123.6 116.1Maximum Tension TMAX = 1.86* TSIG kN 422.9 272.2 258.8 240.1 225.2Change in TSIG or TMAX due to hatches % 100% 95% 88% 83%Static Tension TSTATIC kN 250.0 250.0 250.0 250.0 250.0TOTAL Maximum TTOTAL kN 672.9 522.2 508.8 490.1 475.2Change in TTOTAL due to hatches % 100% 97% 94% 91%Change in TTOTAL % 100% 78% 76% 73% 71%

Open hatches

Table 10: Dynamic hook load: Sea state “B”

Model testsDYNAMIC HOOK LOAD Estimations Hatches

closed # 1 # 2 # 3Significant Tension TSIG = 2*RMS kN 138.1 121.3 115.8 105.3 97.5Maximum Tension TMAX = 1.86* TSIG kN 269.5 240.0 229.1 208.2 192.8Change in TSIG or TMAX due to hatches % 100% 95% 87% 80%Static Tension TSTATIC kN 250.0 250.0 250.0 250.0 250.0TOTAL Maximum TTOTAL kN 519.5 490.0 479.1 458.2 442.8Change in TTOTAL due to hatches % 100% 98% 94% 90%Change in TTOTAL 100% 94% 92% 88% 85%

Open hatches


5. CONCLUDING REMARKS The following conclusions can be made upon the results of

this study:

• Open hatches in the top plate of the suction can significantly increase the hydrodynamic damping, in particular its linear component. This phenomenon could be attributed to strong increase in the pressure drop across the hatch orifice as the local KC number of the orifice flow reduces.

• The increase in linear damping due to open hatches translates into reduction in the dynamic hook load; for the system and vessel properties used in this study the reduction is of the order of 20%. Therefore, open hatches (or other small penetrations) in the top plate can be recommended as means to reduce motions and hook loads, and they should be included in the subsea lift analysis.

• Hydrodynamic coefficients, which are based on the empirical data for steady flow or heaving half-submerged cylinders, underestimate both the heave added mass and the viscous damping for the suction can. The predicted hook load is likely to be overestimated; the error may reach 30%, depending on the sea state and vessel details.

This study shows that small changes in the geometry of

subsea equipment may alter significantly its hydrodynamic properties. For the subsea lift analysis to provide desired accuracy, such changes should be carefully examined and taken into account.

6. AKNOWLEDGEMENTS The authors are thankful to the Australian Maritime

College for providing support to this study.

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