A hydrodynamic analysis method for offshore discharge operations

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June 2008

R,H,M, Huijsmans, iB. de Jonge & O.A.J. Peters Delft University of Technology

Ship Hydromechanics Laboratory Mekelweg 2, 26282 CD Deift

4 TUDeift

Deift University of Technology

A Hydrodynamic analysis method for offshore

discharge operations

by

IB. de longe, O.AJ. Peters & R.H.M.

_Huijsmans

Report No. 1583-P

₂₀₀₈

Published: Proceedings of the ASME 27t1 _{International} Conference on Offshore Mechanics andArctic Engineering, OMAE2008, Estoril, Portugal, ISBN: O-7918-3821-8

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Proceedings of the ASME 27th InternationalConference on Offshore Mechanics and Arctic Engineering OMAE2008 June 15-20, 2008, Estoril, Portugal

OMAE2008-571 55

A Hydrodynamic analysis method for

_{offshore discharge operations}

J.B. deJonge MSc

Dockwise Shipping B.V. P.O.Box 3208, 4800 DE Breda

Netherlands

Abstract

Semi-submersible heavy transport vessels are used for

transport of floating cargo. In general discharging takes place in sheltered and/or very benign areas, which are often not the areas of operation for these cargos. To be able to discharge in less benign areas, an R&D project was initiated to capture the

problems arising at hydrodynamic interaction between two

floating bodies in very close proximity.

Comparison of model tests

with industry standard 3D-diffraction analysis has shown large discrepancies on the motions on the vessel. Therefore, the first stage of this R&D project is to investigate the effect of thenarrow gap between

the loading deck and the bottom of the floatingcargo, find a

better analysis solution and incorporate this in a multi-body hydrodynamic interaction method. To be able to develop this

method, first the single body problem in extreme shallow

water is investigated.

This problem was investigated by Drobyshevski [1], who

assumed that a two-dimensional flow describes the flow in the narrow gap, being the under-bottom domain, for which better

solution methods are available than 3D-diffraction method. His method is tested and validated witha truncated vertical cylinder with flat bottom in extreme shallow water.

Since the Asymptotic Matching Program of Drobyshevski

does not include 3D-diffraction for arbitraiy shaped_structures

and is only applicable for single bodies, the new developed

Multi Domain Diffraction Method is a combination of

two-dimensional: flow and general 3D-diffraction, both based _on linear potential theory.

Nomenclature

A0 = added mass for outer domain A = total added mass

added mass for under bottom domain AMP Asymptotic Matching Program B0 = radiation damping for outer domain

= total radiation damping

B = radiation damping for under bottom domain

b = cylinder radius C1 _{= characteristic length} O.A.J. Peters MSc Dockwise Shipping B.V. P.O.Box 3208, 4800 DE Breda Netherlands Prof. Dr. Ir R.H.M. Huijsmans

DeIft University of Technology Mekelweg 2, 2628 CD DeIft

Netherlands

F0 _{= exciting force for outer domain}

F = total exciting force

FUB = exciting force for under bottom domain

h

= gapheight

H = water depth

HTV = Heavy Transport Vessel

MDDM = Multi Domain Diffraction Method

o

= outer domain

T

_{= draft}

UB under bottom domain

a

= wave direction

p = water density O) = wave frequency

Introduction

Traditionally, the core-business of Dockwise is the transport

of large, voluminous and/or heavy cargo from one harborto another. For many types of cargo, Dockwise is able to use low-effort engineering due to large experience and in-house

developed methods, tools, standards and working-procedures. Still, Dockwise can handle cargos for which extremesolutions

have to be found using high standard industry accepted

engineering methods with the highest safety standards in mind.

Next to the core business, the float-over business is the second tier

in the dèvelopment and execution of the Dockwise

strategy.

In view of the Dockwise strategy, a research project has been

initiated to investigate Offshore Discharge, which means discharging floating cargo at open sea. The research project involves: Commercial relevance Hydrodynamic research Operational procedures Technical/mechanical system Operability analysis

The challenge is to bring the clients' cargo directly to its field

of operation, without first going to a sheltered area and

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bringing the cargo to field with tugs In field, discharge will be restricted by a limiting environmental condition. The basis_for predicting the operability is hydrodynamic analysis,combined with mechanical and structural design. Thispaper only deals

with part of the hydrodynamic research involved in

_the

Offshore Discharge R&D project. Background

In recent years Dockwise has been working on new designs of

heavy transport vessels and has been searching

for new markets. In these studies many model tests were conducted, investigating motion behavior of a very large Heavy Transport Vessel (HTV) with different shapes of forecastles and casings, being the distinguished features of HTV. Also model _{tests of}

typical cargo shapes floating above a fixed box, which was

representing the HTV deck, were performed. Especially these tests confirmed the known difficulty of assessing the motional behavior of cargo in close proximity of the HTV deck. Also, desk-top studies, performing hydrodynamic analysis using 3D-diffraction with multi-body interaction, confirmed the problem of estimating the influence of the narroW gap between cargo and HTV deck.

Tuning of hydrodynamic calculations based on evaluation of the model tests was done by correction of theoretical added mass and damping. However, no clear relation between gap

height and tuning parameters were found. Also,

it was

unknown to which part the tuning had to be divided between error in 3D-diffraction and viscous effects. Uncertainty in the

3D-diffraction results were present, even with extreme fine meshing to ensure convergenceoftheresults.

It is expected that viscous effects do have a large influence on the motions of a body in close proximity of the seabed or of a submerged HTV deck. To find appropriate relations tocorrect for these viscous effects, it is important to start this tuning with correct data from the in-viscid potential flow analysis

This relation must correct for viscous effects only. Therefore it

is valuable to find a method, which is able to derive accurate hydrodynamic data for bodies in very close proximity of the seabed or of a semi submerged HTV. Ultimately this new

calculation method, further referred to

as Multi Domain

Diffraction Method (MDDM), can be used for offshore

discharge analysis and float-over operations in shallow water.

In search of a method to accurately predict the behavior,

several steps were identified. To be able to account for the

narrow gap flow between two hydro-dynamically interacting

bodies, first the problem of extreme shallow water

was

investigated. Drobyshevski [2] followed the way pioneered by Tuck [3] to derive hydrodynamic data for single vertical sided

bodies in extreme shallow water. Drobyshevski so-called

Asymptotic Matching Program (AMP) uses domain splitting

and an

asymptotic matching technique to guarantee a continuous flow over the domain boundary. This method is

only applicable to single bodies with vertical sided walls and flat bottom, not to arbitrary shaped bodies.

Method

Below the so-called AMP is described and

a simplified implementation of the gap flow part of this method into a

standard 3D-diffraction program is shown. During this

research the MDDM is developed and validated with the AMP

and a standard diffraction program DELFRAC fora vertical cylinder in extreme shallow water. Model tests are performed

to validate the MDDM and to investigate the influence of

viscous and other non-linear effects on thehydrodynamic data.

Theory of the AMP

When the under bottom clearance

is

small a standard

hydrodynamic analysis needs a large number of panels on the bottom and near the edges to capture the singular behavior of the flow in and near this clearance, see Figure 1. The AMP is intended to avoid this large number of panels and to provide

high accuracy for any small value of the under bottom

clearance.

1he program is applicable to vertical sided single body

geometries with flat bottom and small clearance compared to

the water depth. The method was tested and validated with analytical data from Drobyshevski [I] and numerical data from Yeung [4]. Increasing accuracy was found, as the gap

height and HITratio decreases

The program uses domain splitting to divide the flow domain in the outer domain and the under bottom domain, see Figure

2. Therefore the three-dimensional problem in the under

bottom domain can be reduced to an integral equation in two dimension. This simplifies the numerical implementation and avoids a large number of panels in the under bottom domain. Continuous flow over the domain boundary S3 is guaranteed by asymptotic matching, which means that velocity potentials are matched in thearea around the boundary S3.

Theory of DELFRAC

DELFRAC is a liñear potential theory diffraction program to perform zero speed hydrodynamicanalysesof arbitrary shaped

bodies. It is based on a three-dimensionalsource distribution

technique for a solution of the linearized velocity potential problem. From this solution wave loads, added mass and

damping parameters are derived, from which motion

responses are calculated, Dmitrieva [5].

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For the numerical computation the wetted part of the hull of

the ship is pane lized with plane elements, SI and S2 in Figure 2. On each element a source singularity is situated. All these

source singularities contribute to the velocity potential, which need to fulfill several boundary conditions. Water particles _are not allowed to pass through the ship hull.

Figure 1: panel model DELFRAC Theory of MDDM

The MDDM was set up as a combination of regular three-dimensional diffraction theoiy and two-three-dimensional flow in

the under bottom domain for single bodies in extreme shallow

water. A combination of the gap flow part of the AMP and DELFRAC is used to perform the hydrodynamic analyses of single bodies in extreme shallow water. To implement these two different solution methods the flow domain is split into the under bottom domain and the outer domain. Surfaces SI and S3 are panelized. Surface S2 is panel free because the

velocity potential and corresponding pressures are derived by the under bottom domain routine, see Figure 2 for a graphical impression.

The governing equations are:

2b

52

,, /,

_{// //}

_//

Figure 2: Definitions AMP and MDDM for a vertical sided cylinder

This is called direct matching between the domains, and is the

most simple way to

couple two domains. Asymptotic

matching, which is used in

the AMP, includes

also information of velocity potential at certain distance from the

domain boundary and is therefore more accurate than direct

matching in case of small gap heights.

Since the linear potential flow theory is used in both domains it

is possible to derive the hydrodynamic data for both

domains separately and add them afterwards. The solution for

the outer domain is discribed by a source layer distribution

over the surfaces S, and S3. For the under bottom domain the theory of the AMP is followed.

Calculation Process

of

theMDDM

The calculation process is divided in four steps, which are

explained in the following

subsections. A graphical

impression, including in and output for each step, can be

found in Figure 3. ( U B-Geometry Panel-model H T w a + Step I Velocity boundary condition Step 2 0-domain 3D-diffraction solver Step 3 UB-domain 2D-potentlal flow solver

FuB, AUB Bu8

3 Figure 3 calculation steps MDDM

Lq0=0

[I]

g?L_w2çoØ

_[2] az òço0 an [3] òço0

0

_5-,;- 'SI

=

[4] Pub [51

Under bottom domain:

Pb

0 [6]

0

[7] Iz=-H

an

[8]

an

'52 [9]

an

I53H53

Pub IS3 =PoIS3 [IO]

tidr bclom dOEnúl ) h

$

Step 4 F,, A,,B,,RAO

(7)

StepOne

First step is the determination of a new velocity boundary condition at the panels on the surface S3. These boundary

conditions result from a unit velocity motion of the body _and

satis1' equation 6. Input of this step is the

_{gap height and}

geometry of the under bottom domain, which is defined by the location of the panels on S3.

Output of this step is the normal velocity at each element on the surface S3. These velocities are non-zero for heave, pitch

and roll and zero for other modes of motion. An example of the velocity boundary conditions for a certain point in time is given in Figure 4.

bound ny conditions at panela on S3 due to haase motion

boundary conditions at panels on S3 dueto pitch motion

Figure 4: example boundary conditions on S3 due to heave and pitch for a vertical cylinder in shallow water

Step Two

Step two of this MDDM is

the

determination of the

hydrodynamic data for the outer domain. A panel model

withoutelements on the bottom S2 is input to the diffraction

program. Additional panels are inserted at ihe location of the

boundary S3, in order to prescribe a new velocity boundary

condition, as given in equation 5. This is an extra boundary condition beside the regular equations I

to 4. Once the

velocity potential is solved, one is able to calculate added

mass, potential damping and exciting forces. Step Three

During step three the under bottom domain solver calculates the two-dimensional velocity potential and derives added mass, damping and exciting forces for this domain. Output

contains the hydrodynamic data for the under bottom domain,

which is the second part of the summation ¡n step four. The

underbottom potential flow satisfiesequation 6 to IO.

4

Step Four

This last

step basically contains the summation of the

separately derived matrices with hydrodynamic data from step two and three.

Verification and Validation

Several calculations were executed

for a vertical

sided

cylinder in extreme shallow water:

Analytical solution Drobyshevski [1] AMP

DELFRAC MDDM

A cylinder with diameterof 40 m was selected, which is in the same order of the beam of the Dockwise HTV. Draft isset to 5 meter and dimensionless mass is 0.785 when calculated with

the equation

11. Five different water depths are used to

investigate the influence of the water depth over draft,

HIT-ratio, on the accuracy of DELFRAC and the MDDM

compared to the AMP. A rigid lid was used for DELFRAC

and the MDDM to avoid irregular frequency peaks in the data.

Table 1: range of calculations for a vertical cylinder

Model tests

Forced oscillation model tests were performed in shallow

water to validate the AMP and the MDDM and are also

performed to investigate the influence of viscosity and other

non-linear effects on the added mass and damping. The tests wererestricted to heave motions.

A cylinder with the same H/T-ratio as used for the potential flow calculations and a scale factor of 50 was used for the

tests. Variations were done for two H/T ratios (1.1,1.2), three

motion amplitudes (25,50,75% of h) and three frequencies

(0.2,0.3,0.4 radIs at full scale).

Vertical forces, acceleration and motions were measured in order to be able to derive added mass and damping from the tests. The signals are band-passed and fitted to a harmonic

signal by using the least sqLiaremethod.

Added mass and damping derived from linear diffraction theory are assumed to be independent of motion amplittide. Viscous effects probably account for non-linear effects and

therefore results from linear potential

theory may be

inaccurate for this cylinder in extreme shallow water. More

insight to the influence of viscosity

on added mass and

damping is gained by varying the motion amplitude.

5% 5.25 m. 1.05 0.25 m.

10% 5.50m. 1.10 0.50m.

20% 6MO m. 1.20 1.00 m.

30% 6.50m 1.30 l.50m.

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Figure 5: model test set up at Marin, Wageningen. Data Comparison

For problems with small gap heights it is known from [2] that the AÌ1P delivers accurate hydrodynamic data. Therefore the

results of this method are used as reference for several

comparisons of different calculation methods.

A comparison between the analytical solution of

Drobyshevski [1] and the AMP will be shown. This calculation is executed for the three smallest HIT

ratios

for surge, heave and

pitch. Only heave

parameters are shown, because surge and pitch are in the same order of accuracy. The program was already

validated by numerical data of Ycung [4]. This will

not be repeated for this specific geometry.

The relative difference between DELFRAC and the

AMP is investigated to locate the problem with linear potential theory in diffraction programs.

The Added mass and Damping coefficients from the

MDDM are validated by using relative difference

compared to the AMP. Results for pitch are also

investigated, but not shown.

The results

from model

tests

have also

been

compared to the AMP.

The data

is made non-dimensional with the following

parameters, where C1 is set to the cylinder radius of 20 m.

-

A.._

B..

4J

B=

[li]

Results

This paragraph shows results of calculations performed for this study to offshore discharge operations. All calculations

are executed for the cylinder as described in paragraph

verification and validation. Amplitude of exciting forcesagree

very well and are therefore not shown. The relative differences in a frequencies range up to 1.0 rad/s are shown.

5

AMP versus Analytical

Added mass and damping for this cylinder is derived by the AMJ and compared to the analytical solution

of

Drobyshevski[1]. Figure 6 and 7 show high accuracy of the AMJ. Therefore this method is used as reference to check the accuracy of the data from DELFRAC and the MDDM.

DELFRAC versus AMP

Relative difference in Heave Added mass and Damping for

five different HIT-ratios is given in Figure 8. For all ratios the

relative difference in added mass is less than ten percent.

Accuracy increases as the HIT-ratio increases.

Potential damping from DELFRAC is derived less accurately than added mass. For heave and pitch the error can amount to thirty percent for the smallest HIT-ratio. Accuracy improves as the HIT-ratio increases. Figure 8 shows the actual problems of the accuracy of damping for structures with this b/T-ratio in

close proximity of the seafloor. Irregular frequency peaks in

the data are caused by the solution from the AMP.

MDDM versus AMP

At lowest H/T-ratio the MDDM computes heave added mass

accurately, see Figure 9. Accuracy improves as the HIT-ratio

tends to zero. This trend is exactly opposite to the trend in accuracy from DELFRAC. For potential damping the same trend can be found. The accuracy of heave damping is equal

for all HIT ratios in this range. These results illustrate the high accuracy of the MDDM and provide a basis for extending the method for multi body analyses. Results for the pitch motion are not shown, but these attain the same level of accuracy for the smallest HIT-ratio. For larger H/'!' ratiosaccuracy for pitch

added mass and damping decreases. Accuracy for other than very small gap heights may be improved by implementing the

asymptotic matching algorithm

instead of using

direct matching.

AMP versus Model tests

Added mass in Figure 10 is derived with a maximum error of ten percent. Large discrepancies occur for the heave damping, which may result from viscous effects. Error increases as the

motion amplitude increases. This could be expected since higher motion amplitudes generate higher velocities in the

gap. An interesting result is given by Figure 11. It shows that

as the motion amplitude decreases the value for damping

becomes equal to the theoretical in-viscid value from the AMP in the limit.

According to the linear potential theory we expect to get a

harmonic force signal when a body is oscillated harmonically.

This is true when the motion amplitude and water velocities

remain small. This is the case at the highest tested HIT-ratio of

1.20, the smallest frequency and the smallest motion

amplitude of twenty five percent of the gap height. This signal can be found in Figure 12. Most non-linear effects occur at the

highest motion amplitude in combination with the highest frequency. In this case the largest velocity values in thegap

occur. The force signal of this test can be found in Figure 13.

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Discussion and Conclusions

Relative error in DELFRAC added mass and damping lies between ten and thirty percent. The relative _{error increases}

with decreasing H/T ratio.

The computed MDDM results agree very well with the results

from the asymptotic matching program. Analogous to the AMP, the MDDM delivers also improving accuracy as the

H/T-ratio decreases. Especially the accuracy of damping has increased significantly compared to the results from

DELFRAC. Thus it can beconcluded that, for a cylinder, with

this bITratio, it is possible to_{use a 2-D potential flow in the} under bottom domain to increase the level ofaccuracy. The

MDDM can be used for single bodies of arbitrary _{shape and} flat bottom. It is expected that this method _{can be extended} easily to the double body case for a real offshore discharge

analysis.

Pitch damping results are not accurate for other

_{than the}

smallest FI/i' ratio. This may be explained by theuse of the

direct matching at the boundary S3 instead _{of asymptotic}

matching.

lt is shown in Figure II that thisnew MDDM is a good base for linearized motion calculations because, in thelimit for zero motion amplitude the AMP and the results of model tests

coincide.

Finally we conclude that the MIDDM

can be used as an

accurate and efficient hydrodynamic analysis method for

offshore discharge operations. Remarks

Extending this method to the double body case is expected to

be relatively easy and should deliver

accurate results for

offshore discharge operations.

The model tests show results' dependant on motion amplitude. This does not correspond with the linearpotential theory. The force signals from the model tests are, in some cases, far from linear harmonic see Figure 13. It would be interesting_to investigate if this is caused by viscous effects solely or if other phenomena occur.

Acknowledgements

I would like to thank my employer Dockwise Shipping _B.V. They gave me the opportunities to perform thisresearch for obtaining the Masters of Science degree. I am also grateful to

Yuriy Drobyshevski because of the good cooperation and

never ending enthusiasm during this R&D project.

References

I. _{Y.DROBYSHEVSKI, 'Hydrodynamic coefficients of} a floating, truncated vertical cylinder in shallow water', Ocean Engineering 31, 2004

Y.DROBYSHEVSKI, 'An efficient method _for

hydrodynamic analyses of a floating vertical sided structure in shallow water', OMAE2006-921 18, 2006

EOWCK, 'Matching problems

_{involving flow}

through small holes', Advances in Applied Mechanics _15,

89-158. 1975

R.W.YEUNG, 'Added mass and damping of

a

vertical cylinder in finite-depth waters', Applied ocean

research 3 (3), p 119-133, 1981

I.DMITRJEVA, 'DELFRAC, 3-D potential theory

inciuding wave diffraction and drift forces acting

_{on the}

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Added Maea Heave

Figure 6: AMP versus analytical

.5 -lo 40 35 30 25 20 15 lo 5 o 2 150 RIT-1.35 -WT2O RIT-1.30 HITIAO

Added Mass, relative difference Deifrac-AMP

Potential Damping, relative difference Delfrac-AMP

Heave

0.4 0.5 0.6

e irad/si

Figure 8: relative difference in non-dimensional heave added mass and damping from DELFRAC

7

Potential Damping Heave

Figure 7: AMP versus analytical

ID -6 -8 10 40 35 30 25 20 15 2 10 $ o -5 -IO o . o )-,. _____ HITI.20 ° WTI.30 H111.40

Added Mass, relative difference MDDM-AMP

Heave

0.1 02 03 0.4 0.5 0.0 0.7 0.8 0.8 e (radIa(

Potential Damping, relative differeno MDDM-AMP

Figure 9: relative difference in non-dimensional heave added mass and damping from MDDM

(11)

20 lo 20 15 10 Io Io 14 12

r:

Heave Added Moss 14/7=1.1

AMP

-0-model teed, ampI 25% of h -f-model tesi, ampi = 50% of h

-'14-'- model test, ampi = 75% of h

8,15 02 0.25 03 035

freqy at SI scale tradlef

Heave Added Mace HIT=I.2

'AMP

-0-model test ampi 25% of II -I-model test, ampi 50% of h

-44-model test, ampi = 75% of h

818 02 0,25 03 0.30

frademoS .1 frI acole tradii Heave D.n35ng HFTst.l

AMP

"0-model test, ampia 25% of h -I-- model test, ampi = 50% of h -li- model test, ampi = 75% of h

Heave OssOurU, 1411.1.2

03 0.35

frscatooy 0151 scale (radd(

AMP

'-0--model tact, ampie 25% of h

-f- model lest ampi = 50% of s 'ie-flmdel test, ampi c75% 01h

815 02 025

Figure 10: heave added mass and damping model test compared to the asymptotic matching program

J

15

to

5

00

'leave Despeg, Htl'=t.I, fre.4 mdli

-

AMP

"0- model lest

Figure 11: dimensionless damping as a function of motion amplitude 25 20 15 lo

jo

.5 'lo -15 25 40 FZ(l(, freql.414 md/s. ampv2ti% 01h, 4Jfc12

_ bonsipassed fo(ce signal calculoted Force from motion ltq fit

20'motlon sq fil

IA AWl

41 42 43 44 45 40 6mo (ai

47 40 49 50

Figure 12: harmonic force at model scale, calculated force from least square fit method and motion signal from model testsa

FZ(t), freq2.828 cod/s. omp75% of h, HIIcl.2

Figure 13: non-linear force at model scale, calculated force

8 _{from least square fit and motion signal from model test}

04 0,45

0.4 0.45

0.4 t45

0.2 0.25 0,3 0.35

freqeency al 51 amIa (mdii

04 0.40

to 20 30 40 50