Deift University of Technology Ship Hydromechanics Laboratory Meke!weg 2, 26282 CD Deift
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Deift Ufliversity of Technology
The influence of a free surface on passing Ship
effects
by
l.A. Plnkster
Report No. 1412-P 2004
Published In: lflternatlonal Shipbuilding Progress, ISP, Marine Technology Quarterly, Volume 51, Number 4, 2004 Publisher: Deift University Press, ISSN 0020-868X
Page lof 1/1
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internatona1 Shipbuiling Progress
ISSN (print): 0020-868XISSN (electronic): 1566-2829
Editor-in-chief
Prof.dr.ir. J.A. Pinkster, Deift, The Netherlands
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fr. H. Boonstra, Deift, The Netherlands Prof. A. Francescutto, Trieste, Italy Prof. J.J. Jensen, Lyngby, Denmark Dr.ir. J.O. de Kat, Wageningen,
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Volume 51, no. 4
J.A. Pinkster
The.influence of a free surface
on passing ship effects
313
M.R. Belmont, K. Bogsjö, J.M.K. Horwood and R.W.F. Thurley
The effect of statistically dependent phases in short-term prediction of the
sea: a
simulation study
339
J. Dang
Improving cavitation performance with new blade sections for marine propellers 353
A. Millward
EH-'ECTS
J.A. Pinkster
Department of Marine and Transport Technology, DeIft University of Technology,
Deift, The Netherlands
mt. Shipbuild. Progr., 51, no. 4 (2004) pp. 313-338 Received: October 2003.
Accepted: March 2004
Ships moored in harbours are subjected to hydrodynamic forces due to other ships
passing nearby. These hydrodynamic forces induce motions of the moored ship which may hinder loading/discharging operations or cause damage to the mooring system
These low frequency forces, sometimes known as suction forces, are associated with
the primary pressure system around the sailing vessel which acts upon the moored
ship. These effects are not to be confused with forces due to the secondarywave
sys-tem,, or wash waves, of the passing ship. The latter are a relatively high frequency
phenomenon and will not be treated here. This paper adresses two methods to predict the low frequency forces due to a passing ship, the first of which is based on
imple-mentation of the so-called 'double-body'flow method introduced by other authors.
Double-body flow methods have been shown to be effective in predicting passing ship forces on a ship moored in open'water However ships are rarely moored in open
Wa-terbut rather in harbours with amore orless:complexgeometry whichis orders larger
that the Ñhips involved. Ships passing through ha rbours besides generating forces oñ moored ships also generate long-wave activity or seiches in harbours. These are due to the discontinuities in the harbour geometry which are almost always present. The second method treated in this paper is concerned with prediction of passing ship
ef-fects which take into account the generatiOn of seiches due to the passing ship and
the forces these exert on the moored ship. Results of both methods are compared with results of model tests for the case of a ship moored' in open water Both methods are subsequently applied to cases involving a complex harbour geometry. Results of com-parisons of predicted horizontal forces on a moored ship show the additional effects
1.
Introduction
Passing ships create disturbances in the water which result in forces on other ships
and floating structures. Such hydrodynamic forces can result in high mooring forces
and unacceptable motions ofthe moored vessels. In extreme cases mooring lines of
ships have parted which in one case, see NTSB report [ 1 1,resUlted in loss of life 'and
total loss' ofthe moored ship dueto fire. Such cases areextremelyrare but hindèr and damage dûe 'to passing ship effects are a regular feature of life along the waterways and in harbours. With the increasing awareness of and decreasing tolérance relative to personal injuries, environmental impacts 'and damage to facilities and ships, more attention is being focussed on evaluation' of such effects whenever major changes are made with respect to the vessels plying the waterways (larger, faster), the waterway geometry or traffic volumes.
At the Delft University of Technology research has been conducted into methods to
predict the effects of passing ships on moored vessels. Such effects have in the past concentrated on suction effects associated with the primary or "double-body" flow around the passing vessel. 'See for instance King [3]. By definition, this means that
real free-surface effects, i.e surface wave propagation effects, are not accounted for. The reason for basing the effects of passing ships on double-body flow models is that
generally such ships are moving at low Froude number values,, even when viewed
in relation to the waterdepth. However, depending on harbour geometry, even in the case of large, slow ships, the disturbancecreated by the ship may setup;seiches in the harbour which will also have their effect on moored vessels.
A study carried out by the Ministry of Transport and Waterways in the Netherlands [2], based on full scale measurements, showed that large inland barge combinations (10000 t) entering a long canal from relatively open water are capable of generating solitary waves which propagate through thecanal system ahead of the vessel causing unexpected rises in free-surface elevation resulting in' damage to moored vessels. In this particular case, the bargecombinationcausing the damage was still several miles away from the affected vessels.
In this contribution attention isfocussed ntwo:models topredict the effects of passing
ships,, one based on the 'clàssical' double-body potential flow model and one also
based on potential flow but taking into account free-surface 'effects for large passing ships moving at relatively 'low speeds.
In 'effectthe second model makes use of a double-body flow model to determine the
time records of fluid motions and pressures due to a passing vessel at the location
of the moored vessel and the fairway boundaries. Subsequently, passing from
time-domain tothefrequency-time-domain thediffraçtioneffects(including free-surface effécts) are solved by means of a 3d, multi-body diffraction code. Fiflally, all results are
free-surfaceeffects.
In the case of large, slow ships, it will be seen that the freesUrface effects are due to the surrounding harbour geometry being excited by instationary water motions arising from the,, essentially double body flow pattern moving with the passing ship. Neither of the models mentioned here constitute complete models of the phenomena involved In the case of the double-body flow model, the free-surface is neglected while, within the potential flow context, the shipship interaction is fully accounted for. In the case of the second model, free-surfaceeffects are partially accounted for while the interac-tion isrestricted to theeffect of the passing shipon the moored ship,, and the presence of the moored ship does not effect the passing ship.
In the following both models will be introdúced and subsequently some comparisons will be made between results.obtained using both models. It is assumed that the flow around the passing. ship, moored shipand in the waterway can bedescribed by means of potential flow i.e the fluid invisëid, incompressible and homogeneous and the flow is irrotational. For both models,, restricted waterdepth is taken into account.
2 Doubie-body'model
The model is similarto that described by Korsmeyer et al [4] in that it is based on 3-dimensional potential flow. Forthe doublebody flow model, the potentials describing the flow are based on the Rankine source formulation taking into account restricted
waterdepth and a rigid stil water level. To this end the Rankine source formulation
needs to be modified to take into account the zero normal velocity which is applicable at both the stil water level and the bottom of 'the waterway. This implies that sources are mirrorred an infinite number of times about both the free surface and the bottom. Wehave made use of the formulationgiven by'Grueand Biberg[5]. The infinitemirror series is replaced by a polynomial representation thus making the computations 'less
demanding in terms of time. The doublebody flow model is suitable for computing
interaction forces 'in 6 D.O.F. on multiple vessels, taking 'into account the harbour or fairway geometry. Vessels which are sailing are assumed to sail on a straight course at constant speed. The computations make use of 3-d panel models of 'the vessels and the harbour geometry.
2.1. Theory
Useis made of two systems of axes; i.e. an earth-fixed,O X1 - X2 - X3 systemof axes in which the potentials' and the motions of the center of gravity of the bodies(ships) are'expressed and, for each' independent body, a body-fixed ox1 - x2- x3 system of
axes in 'whiôh the body geometry 'and the resultant forces and moments on each body are expressed.
The co-ordinates of a point on the wetted part of a body isdenoted by in the body axes and by 2,, in the earth-fixed system of axes in which m denotes the body in ques-tion (m = 1, M). The co-ordinates of an arbitrary point in the fluid dômain is referred to the earth-fixed.axes by .the vector . The positive direction of the unit normal
vec-tors to the wetted part ofthe hulls is into the fluid.
The computations of the hydrodynamic interaction forces are basedon 3-dimensional potential theory. The flUid is assumed to be inviscid, incompressible and irrotational.
Due to the fact that there is no free-surface and therefore no memory effects are
present, all quantitiesare real-valued.
The governing equations for determining the potential flow are as follows: - The equation of continuity or Laplace equation:
(1)
- The normal velocity condition at the (honzontal)sea floor (X3 = h):
¿IX (2)
- The normal velocity condition at the mean waterlevel (X3 = O):
dx
(3)- The no-leak condition on the hull surface of all bodies:
db
flm
= Vm.flm (4)
in which V' is the velocity vector of body-m and is the normal vector of the wetted surface of body-rn.
2.2. Solution for the potential problem
The potential flow problem can be sOlved by introducing a distribution of sources on all bodies:
=
Idi
115mÁm,Am15m
(5)in which:
a(Am) = the strength of a source located in A, on the wetted surface of body-rn.
G(e,Am) = Green function of a source in A relative to the potential value in .
For the Green's function we have chosen the following formulation which satisfies simultaneously Laplace's equation (1), the sea-floor condition of equation (2) and free-surface condition of equation (3). We refer to Grue and Biberg [5] for further
details.
The boundary condition on the hull of each body is given by equation (4). Substitution of equation (5) in equation (4) gives:
-a(im)±
Jjc7(An)_G(An)dSn
= Vrn.?im (6)The method for solving this problem is treated in the next section.
2.3. Numerical aspects
By discretising the mean wetted surface of a into N panels on which the source
strengths are homogeneously distributed the following equation is found for the nor-mal velocity on the k-panel on body-rn:
0(mk)+
a(Aflj)G(Rmk,Afl.)ASfl.= 'm.flimk (7)body-rn and the source strengths a(Â,1..) on all other panels of all bodies. The total
In the above equation, theunknowns are the source strength a(mk)On the k-panel on number of unknown source strength in the above equation is equal to the sum of the number of panels on all bodies. However, similar equations can be setup for all other
panels on all of the bodies. In these equations the same unknown source strengths play a role. This means that we obtain a simultaneous set of linear equations in the
unknown source strengths which can be sol ved using standard methods.
Due to the changing relative position of the vessels and the fairway geometry, equa-tion(7) is solvedfor discrete time stepsas the vessel passes For each relative positiOn
source strengths etc. are obtained for later use in determining fluid velocities and
interaction forces.
2.4. Hydrodynamic forces
The pressure in a point on the wetted surface f a moving vessel (body-rn) can be
determined baséd on Bernoulli's equation:
p = p
-
p(IbI2
-
(8)In this equation the fluid velocity 4refers to the velocity relative to the moving
only linearmotions in the horizontal plane are considered.
The hydrodynamic forces.on body-rn are foundby integration:ofthe pressure overthe mean wetted surface'ofthe body:
Pm=_JJPiimdSm
(9)Taking intoaccount equation (8) results in:
Pm
hJ5m_P
ÜmdSm_jj_p([/(bJ2_ ItmI2)
ñdS
(IO)Which may also be written as:
Pm
=
JJSm « dSm)-
f/ _P(II2 - Im!2) ñm dSm
(11)The first term in equation (li) represents the unsteaiy part of the interaction forces
and moments in that it is dependent on the rate of change of that part of theequation. The second contribution is solely dependent on the instantaneous velocity distribution around a vessel.
In cases where the position of a vessel relative to other boundaries does not change, for instance a long quay-wall parallel tothe sailingdirectionofa vessel, ora vessel sailing in shallow water of constant depth, the first contribution is zero and only the second
contribution remains. In the general case of changing geometry, both contributions
are relevant.
The potential c1contains contributions due to all vessels. Each vessel contributes to the total potential through components:due to each mode of motion Thesearea linear function of the velocity of the relevant motion components:
M6
YPnk'"nk (12)
n=lk=1
In which:
Vflk = Velocity component of for the k-mode. In our case only straight line motion in
the horizontal plane is considered, ie. k = i, 2
Pnk = Potential due to unit motion velocity in the k-mode of. We now define the coefficients amjnk
amink = ' 115m Pnk mjdSm (13)
The coefficients amjflk are in fact added mass coupling coefficients relating accelera-tion of in the k-mode to the ensuing force on body-rn in thej-mode
Combining results of equation (12) and equation (13) in equation (li) gives the fol-lowing expression for the forceon body-rn in the j-mode:
Fmi = -
±
(amjflk.Vnk)-
JJ
P(II - Iml2) t2mj dSm
(14)n=1k=1 5m
It is clear that the second part of equation (14) is a quadratic function of the fluid
velocities whichare,in turn, linearly related to the velocity of the vessels. The firstpart of the equation can also be shown to be quadratic in the vessel speed by considering that if the velocity component Vflk is constant the timederivative operateson the added mass coupling coefficients of mmjflk. This can be written as follows:
damink damjflk
(15)
dt
ds
dt
The gradients of the added mass coupling coefficient along the track of the
vessel are speed independent. In equationi( 15) 1f is the velOcity of the vessel-n along its track. Since this is equal to ItnI,, the first term of equation (14) is shown to also be a quadratic function of the ship's speed
The potential nk is found as the solution to the following boundary condition on the for the mode-k:
dçbflk
nk (16)
in whichnflk arethe cornponents of the generalised normal vector tothe wetted surface
S of:
nfl1cos(fi,x1)
= cos(i,x2)
nfl3 = cos(i,x3)
nfl4 = X2fl3X3fl2
=
X,1'fl,3 = Xfl1flfl2Xfl2flfl1 (17)As indicated in the previous section, the potential problem is solved for discrete time
steps and the source strengths etc. are retained. At each time step the second part of
equation( 11) can be evaluated. The first part involves determining the gradient of the added mass coupling coefficients amjflk. This is obtained by applying a cubic spline to the discrete values obtained for all time steps.
*1f
Figure 1: Passing ships.
2.5. Application of double-body model
Mrsd 100 kM*II
t
SU
Figure 2: Surge force on 100 kdwt tanker
In this section we shall apply the double-body model to the surge and sway forces and yaw moment on a moored tanker in shallow water in order to show that, for the case of a vessel moored in open water, this model gives a good approximation for the passing ship effects.
The results of computations will be compared with results of model tests carried out by Remery [6].
The results apply to a moored loaded 100 kdwt tanker being passed by a loaded 30
kdwt tanker at a distance, measured board-to-board, of 30 m. The set-up is shown in Figure 1. The main particulars of the vessels are given in the following Table.
The waterdepth amounted to 18.05 m being 1.15 times the draft of the moored tanker.
The model tests were carried out at a scale of 1:60 in the former Wave and Current
Basin of MARIN. This facility measured 60 m x 40 m so the passing maneuver can be considered as having taken place in horizontally unrestricted waters. The passing speed in the model test corresponded with 7 kn. full scale.
The computations were carried out using panel models for the tankers which had the
same main dimensions as the models used in the tests. Actual body plans were not
available so the panel models do not conform exactly with the model hull shapes. The total number of panels on each of the tankers amounted to 388. By modern standards this is not a particularly high number but is adequate for the purpose at hand.
1
í.wr
Vessel deadweight tons 30 k 100k Length between pp m 183.00 257.00 Breadth m 26.10 36.80 Draft m 10.50 15.70 Displacement m3 40,200 118,800 o t XIL, 3 1 2
£
Sway (erce
10000
.15000
Yaw moment
Figure 3: Sway force 100 kdwt tanker Figure 4: Yaw moment 100 kdwt tanker
The results of the model tests and computations are given in Figures2through 4 in the
form of the relative position dependent surge and sway forces and yaw moment on
the moored vessel. The relative position has been made non-dimensional on the basis of the mean length of both vessels and the forces and moment have been divided by the square of the velocity of the passing vessel. A negative distance - indicates that the passing vessel is approaching the moored vessel. At zero the midships are abreast.
The results shown in Figures 2through 4 show that the double-body model gives a
good approximation of the forces on the moored vessel. The measured amplitudes
of the surge force and the yaw moment are slightly larger than the computed values. Remery [6] carried out a comprehensive set of tests in which the passing ships, passing
distances and ship's speeds were varied. We have shown comparisons for just one case. Korsmeyer et al. [4] have also shown comparisons of the double-body model
with model test results which are in keeping with our findings. The conclusion is then
that for the open water case, the double-body model gives a good prediction of the
passing ship forces.
With respect to the main characteristics of the forces and moments we note that as
the passing ship approaches there is at first a repulsion phase in which the surge and
sway force directions and the yaw moment indicate that the moored vessel is being pushed aft and to port. This phase starts at about 2 ship lengths distance and ends
at one ship length distance for the surge force and 0.5 ship lengths (ships with bows
abreast of each other) for the sway force. The yaw moment switches sign so that at
about 0.5 ship length separation, the yaw moment is drawing the bow of the moored ship towards the bow of the passing ship. Maximum sway force is reached when the
midships of the vessels are abreast. At this point surge force and yaw moment are
close to zero. As the ships draw apart, the sway force reduces and shows a repulsion peak at around I ship length distance. At 0.5 ship length the surge force has changed
In
IM
Inn o X lt._ -I 2 2 s .3 -2 -1 o s XI Çso 25 so .3 .2 -1 Surge force o x,t 2 loo
Jo
:.toQ -zoo .3 - TatoUes.- - Exdudng outIls term -2 -t
Sway force
o 2
Figure 5: Break-dòwn of surge force. Figure 6: Break-down of sway force.
sign so that the force on the moored ship is in the direction of the passing ship. At around 0.5 ship length the yaw moment tends to turn the stem of the moored ship towards the stern of the passing ship. As the separation distance increases we again have at between i and 2 ship lengths, a repulsion phase in which the moored ship is
pushed in a direction away from the passing ship.
An aspect we would like to draw attentiOn to is. the contribution to the total forces/ moment of the components of the force equation (14) in other words, which terms in
the equation really count. The first part of the equation is a term dependent on the added mass and added mass moment of inertia coupling terms. This part expresses
the effect of the rate of change of fluid momentum on the forces. The second part of the equation expresses the influence of the pressure drop related to the fluid velocity. It should be notedthat the second term in the second part involving i'm is equal to zero sincethe velocity ofamoored vessel is equal tozero. The excitation due to the second
part of the force equation is only from the fluid velocity squared term. In Figure 5 through 7 we show the computed results of the surge and sway forces and the yaw
moment on the 100 kdwttanker again. The passing distance is stil 30 m. Each figure
shows the total computed force or moment and the second part of equation (14). It is clear from the results that the first part of equation (14) is dominant and that the
second part (also known as 'Venturi' effect) is small. 3. The free-surface model
The purpose of this model is toobtaininsight.in the.dynamic response of moored ships
due to passing ship effects fär the case that the passing ship excites low frequency
seiche- or solitary wave-like wave activity as it passes through the fairway/harbour. Existing models based on double-body flow explicitly exclUde such effects while at
the same time it is known that good predictions of interaction forces have been
ob-tained using this model. Most correlations, however, are based on comparisons with
Yew moment
Figure 7: Break-down of Yaw moment. Figure 8: Surge force on 100 kdwt.
model tests on mooredships in open water. See, for instance, Remery [6]. This model
does not take into account short surface waves or so-called wash effects due to the
passing ship. These effects will be treated in a seperate paper. Both models have been introduced by Pinkster and Naaien [7].
The computationaiprocedure is summarized in thefollòwingsteps in which undèrly-ing assumptions will also be highlighted:
I . The effect of a passing ship (or of passing ships) on moored ships is based on
one-way action. The flow about the passing ship is notaffected by the presence of the fairway or moored ships.
A passing shipcauses,, relative to a fixed observer (ie. the moored ship), transient
flow which can be described by a double-body model applied to the flow about the
moving ship This assumption is prompted by the knowledge thät double-body flow Ias been successfully applied to the interactión forceproblem forships in open water.
In thiscase theflow induced bythe passingship is determined neglectingthepresence of the moored ships and the fairway/harbour boundaries but taldng into account the
restricted waterdepth.. This results in the "undisturbed" flow induced by the passing vessel. If only one passing shipis involved, this flow is time-independent with respect to the passing ship but transient relative to the moored ship and the fairway/harbour. With only one passing shipthe double-body flow about the vessel is solved onlyonce. If more than one passing ship are involved, the dotiblebody flOw (involving only the passing ships) is solved for each time step
The transient flow dúe to a passing ship, or passing ships, can be expressed in terms of time-dependent normal velocity and "undisturbed" pressure at the location of the collòcation points of the panel models of moored ships and fairway/harbour. This is affected by multiplication of the source strength vector for the passing vessel found at each step by the matrices of influence coefficients for the pressures and velocities at the locations of the collocation pòints of the moored ships and the fairwayIharbour
'wJ o
-4
mom1111
-2 -1 o Surge force 50 -- ßoubte--boctj 26 -50 -2 o XA -1 2 3If only one passing ship is involved, the source strengths are time-independentwhile, due to the changing position' of the passing ship relative to the moored shipsetc. the
matrices of influence coefficients are recalculáted at each step.
The time-dependent normal velocities and pressures on the grid of the fairway and the moored ships can be resolved into theircorresponding frequency-domain compo-nents by means of FFT. Before doing, so however, we must take into account the fact that if'the passage of a passing vessel sets up significant seiche activity, the question
remains,, how long seiches taketo dissipate. This is of importancebecause (see
sub-sequent steps) the procedure followed here renders results which are periodic in the fundamental time interval This interval must be taken sufficiently long, for all
tran-sient disturbances set up by the passing vessel have died out (memory effects) The
time interval ofthe passiìig shipevent can:beincreased by padding withzeros the time domain "input" beyond the passage time of the passing vessel. In practice, depending
on the geometry of the fäirway etc. passage times of the vessel are increased by a
factor ranging from 2 to 8. FFT of the time records results in a considerable number of frequency components.
Let us assume that the time interval' of significant excitation (induced fluid velocities
and .pressures) due to the passing ship amounts to T = n Ar in which n equals the
number of discrete values and Ar equals the time step. We chose n to be a power of two for the sake of the FFT We estimate, as an example, that the seiche phenomena will last four times longer than the passage time T. All velocity and pressure records
are extendéd by zeros so that the total simulation time becomes T =4n At. Subse
quent FF1' of all time records yields 4 = 2 n complex frequency components with
frequencies from s to being the Nyquist frequency.
Using the multi-body,,linear 3-d diffraction code DELFRAC, see Pinkster [8], ap-plied to the moored vessel and the surrounding fairway/harbour,, the diffraction
po-tentials can besolved forthe right-handside normal velocity vectors obtained from
step 4. The diffraction potentials do not take into account the passing vessel. The ra-tionale behind'this is that passing ship effects generate low-frequency waves (seiches)
mainly through the diffraction effects from the fairway boundaries Such waves 'are
long and the passing ships are small in relation to these wavelengths and thus do not
modify diffraction effects. Due to the extension of the simulation time (see step 4)
as a result of expected memory effects, the number of frequency components which
have to be solved can be quite large,, up to several hundred frequencies. However,
the free surface effects are restricted to rather low frequencies so that in many cases satisfactory results are obtained for between 25 to 350 frequencies depending on the particular case.
6 The total velocities, pressures, fluid forces onthe moored ships etc. can be obtained by adding the double-body components (inconling disturbances) and' the diffraction components.
7. By the application of Inverse FF1' timerecordsof all relevant.data suchas
waveel-evatións,, fluid velocities, passing ship forces and moments,wave elevations etc can be obtainecL These will be obtáined for the same for the same time steps and total
duration as selected under step4.
The procedure outlined here involves a flow Which is the superposition of a double-body flow which complies with the rigid lid condition at the mean free surface and a free-surface flow which complies with the linearized free surface condition. This in-consistence may be acceptable if We bear in mind that thedominant flow about large, slow ships, is not of the freelypropagating kind. Free surfaceeffects in terms of wash
waves are small and do not play a role in the passing forces on other, lärge moored
ships. The ability of a double-body flow to generate waves is due to the fact that
nor-mal velocities are generated atthe location of the grid of the surrounding harbour and moored ship. These normäl velocities are counteracted by the free-surface potential flow. The assumptions made in this procedureare not verifyable based on comparative computations but need to be validated by comparison with results of model tests. The computationalprocedure is based on the use of the frequency domain 3-ddiffrac-tion method along with the FF1' and IFFI' techniques to make the transposi3-ddiffrac-tion from time tofrequencyand fromfrequency to time. The same resUlts cöúldalsobeachieved by solving the diffraction problem directly in the time domain. We have chosen the
present solution procedure due to the availability of a well-tried frequency domain
diffraction code.
3.1. Multi-body diffraction theory
In this section we give a brief overview of the main aspects of the 3-d, frequency-dómain, diffraction theory and the coupling with the double-body flow computa-tions To this end we consider m = 1, M bodies being the moored vessel(s) and the fairway/harbour geometry which is also considered as a seperate (fixed) body. The moored vessels however, can move under influence of passing ship forces and
mo-ments.
The motionsof the rn-body in thej-mode relativeto its body axes aregiven by:
Xmj(t)=Imje_b0)t (18)
in which the overline indicates the complex amplitude of the motion expressing that a quantity has both amplitude and phase characteristics. In the follOwing, the overline which also applies to thecomplex potentials etc. is neglected.
The fi id motiónsaredescribed by the tótalpotential as follows:
The complex potential 4 follows from the superposition of the frequency components
of the 'undisturbed' incoming flowdueto thepassing ship Ø,, asobtained after FFFof
the time records, the wave diffraction potential d and the radiation potentials associ-ated with the resultant motions of the bodies çbmj:
M6
ømjXrnj} (20)
m=1J=1
It should be noted that in the classic 3-d multi-body formulation for the potential, the contribution is replaced by Ø being the undisturbecFpotential due toa regular
long-crested wave andthe term
+
Ød) scaled by the amplitude a of the regular wave.In our case there is no independent scaling factor for the potential dùe to the passing ship i.e. it derives is amplitude directly from the FFT-operatión.
From the double-body computations the value of the potential 4.,,. due to the passing
ship is obtained at all collocation points of moored vessels and the fairway/harbour
for each time-step from the following equation:
(2)=
JJ a(Am)G(2,Árn)dSm
m=1 Sm
M,
(21)
In which the summation is over moving vessels only and the vector 2 denotes the
co-ordinate fa collocation point on a moored vessel or harbour.
Time records of velocity components due to the passing ship are obtained using the
double-body solution, for example, for the x-velocity component:
ps(2)
,JJ
O'(Âm$G(2,Am)dSm (22)m=1 X
The resultant time records of the potential and velocity in a point are,, after
exten-sion by zeros as needed, transformed into complex frequency components Ø,,(w) nd
V5(w) by means of the Fast Fourkr Transform technique. We then transform the
frequency components in order to comply with the definition for 4i, as applied in the frequency-domaindiffraction computations, see equation (20):
=
-4--5(w)
(23)The same transformation is applied to the velocity components. Knowing the
fre-quency domain components of the potential and the related velocity components
the diffraction potential dcan be determined based on the no-leak condition:
dçb
an
1nkIn which is the frequency component of the normal velocity induced by the
pass-ing ship at the collocation points on the moored vessels and harbour geometry. The radiation potentials are determined based on the no-leak condition while oscillat-ing the moored vessel in the k-mode:
(25)
±
{0)2(Mmjnic ±amjnt) Wbmink±Cmjnk}Xnn=tk=1 =Fmj
(31) Thecorresponding normal velocityequation forsolving»the unknown source strengths
is as follOws:
O(m)
+
Jj a(Ân)-G(2m,An)
dS =
(26)In the above the a values are for the diffraction or radiation case depending on the chosen value for the right-hand-side.
Having solved forthe source strengths, the potential in a point becomes:
(Í)
n'
Jj a(Äm)G(,Äm)
dSm (27)Knowing the potentials, the fluidipressure follows from thelinearized Bernoulli
equa-tion:
p(,t) = p =p(Í)e0)t
(28)The complex amplitude of the pressure follows from:
p()=p=pw2{(p±d)+
ç)mjxmi) (29)m1 j=I
The exciting:forces follow fromthe integration of the 'undisturbed' pressure due tothe
passing ship and the pressure associated with the diffraction potential over the mean
wetted surface:
= _P
w211S (4p+çbd) m dSm (30)Thecomponents of 1m are given by equation (17).
It is also possible to compute the motions of the moored vessel due to the passing ship effects. If the hydrodynamic properties (damping, mooring stiffnesses ) can be
considered as being linear, the equations of motions for body-rn in the j-mode become as follows:
In this equation M,a,b, c denotethe mass, added mass, dampingandspring coefficient matrices respectively, Fmj isthe i-component of the force vector Pm in equation(30)and Xnk are the complex motion amplitudes of in the k-mode.
The spring coefficient.matrices.contain hydrostatic and mooring system restoring terms. The hydrodynamic components of added mass and damping follow from:
am ink = 'R{p
1m
nknmi dSm}bmjnk
=
"Sm kmj dSm}
(32)The solution to the diffraction and radiation potentials, and nk respectively is ob-tained by a zero-order panel method based on a distribution of wave-making sources over the mean. wetted surface of the moored vessels and the fairway/harbour
geom-etry. The same basic equations apply as are valid for the double-body problem, see equations (5) and (6) In this case, however, beside satisfying the no-leak condition
for the bottom, the Green fúnctionsconform with the linearized free-surface:boundary
conditiOn:
.0
(33)The form chosen for the Green function is, among others, given by Newman [9] but will not be dealt with further here.
3.2. Effèc: of ship's speed
The exciting forces on a moored ship due to a passing ship are computed using equa-tion (30). It can be shown that for the case that free-surface effects are negligible, this
force is also a quadratic function of the speed of the passing ship.. We consider the
case of a single passing ship sailing at a constant speed or at a higher speed U1 and the forces it exerts on a moored ship.
Equation (12) shows that the time record of the potential due to the passing ship is a linear functiOn of the speed:
A. - A.
-
(34)o
Due to a higher passing speed the passing event takes place in shorter time i.e. the
components present in the time records of the potential are also a linear function of
the speed: U Wi = WojL
o
F.FT of the passing ship potentialsresults in frequency components 4. A component with frequency w0 at speed U0 corresponds with a component with frequency w1 at speed U1. The amplitude is linearly transformed as follows:
Ø3(w1) =
Taking equation (35) and equation(36) into account, equation (23) becomes:
=
iw=
, -lW-1 '-'O o=
_44Pp(W0)=(W0)
(37)Equation (37) shoWs that the complex amplitude of a frequency component of the 'undisturbed' potential is independent of the speed of the passing ship. Under the
assumption that the free-surfaceeffects are negligible, the complex amplitudes:of the corresponding diffraction potential components will also be independent of the
pass-ing ship's speed. See equation (24). The complex amplitude of the components of
the passing ship force is given by equation (30). On the basis of the above reasoning, the value of the integral on the right-hand-side is unchanged by speed. However, the
value of w isproportiónal tothe passing shipspeed and as a consequencethecomplex
amplitude of the force is proportional to the square of the speed.
This conclusion isonly valid for the case that free-surface effects arenegligible. When this is not the case, the speed dependency of the passing ship effect need not be purely quadratic.
In the following sectionsome applications of theaforegoing model will be treated and results of computations compared with results based on the double-body flow model in order to illustrate the free-surface effect.
3.3. Application offree-surface model
We will now apply the mixed double-body/free-surface model to the passing ship problem. First of all, since the pure double-body solution gives good results for the
open water case comparedto theresuitsof model tests, (see Figure 2 through Figure 4) we require that the new model should' also give the same results. In Figure 8 through
100 E 200 .3 Sweyftrce I.ocu, olC.nterofGravfly Yaw moment
Figure 9: Sway force on lOO kdwt. Figure 10: Yaw moment on 100 kdwt.
4ofrn
Figure 10 the result of computations based on both models are given for the same case as before. These results show that for the open water case the new model gives results which are almost identical to thedouble-body model. Even though the passing
distance between the ships is small, the assumption of one-way-action for the free
surface model appears to hold well. It can be concluded that the new model is capable of predicting passing ship effects in openwaterandthatin thiscase free-surface effects
are negligible. Additional results of the computations based on the new method are the motions of the stationary vessel. In Figure lIthe locus of the center of gravity
of the moored vessel is shown for the case of a free-floating vessel without restraint from a mooring system. We see that the motion is almost circular, the greatest sway motion, away from the track of the passing vessel, occurs when the passing vessel is abreast of the stationary vesseL
The second case concerns a fully loaded 200 kdwt tanker moored alongside a long,
straight, vertical quay wall along one side of the track of the passing vessel. The other side of the track is unrestricted. The passing ship is identical to the moored ship. The main particulars of the vessels are given in. the following Table.
&
- Dbody
5000 maimii
.3 2 -1 2 .1 o ngsb mVessel deadweight tons 200 k
Length betweenpp m 31000
Breadth m 47.14
Draft m 1890'
Displacement
m3 234,826
The waterdepth amounted to 22.68 m and the passing distance, measured from
cen-terline to cencen-terline amounted to 270 m. The gap between the side, of the vessel and the quay amounted to 3 m. An overview of the situation is shown in Figure 12. The passing speed amounted to 4 rn/s.
Since we are simulating a 'ship moored along a long, straight quay, we assume that
the passing vessel approaches from a long distance along the given track and that no
effects due to a limited quay length or from acceleration effects of the passing ship are present. To this end computations based on the free-surface method start by a
gentle increase in the speed of the passing ship from zero at a considerable distance
from the moored ship. In this way transients, which express the instationary free
surface flow generated by the quay as a result of rapidly changing'flow velocities due to the accelerating vessel', are avoided. This need not be applied in the double-body
case since this contains no memory effects. The results of computations of surge
force, sway force and yaw moment based on both computational methods are shown
in Figure 13 through Figure 15. These results show that the surge force,sway force and yaw momentare almost identical. As in the previous case, we show the locus of the center of gravity of the stationary vessel for the free-floating case in Figure 16.
We see that compared to the case shown in Figure 11, the locus 'is a much' flattened
ellips with by far the largest motion occurring in the direction parallel' to the quay.
Even though there' is no mooring system, the hydrodynamic excitation forces and the reactiOn fOrces act to keep the vessel from large displacements in the direction of the quay. In Figure 16 we have also includedthe 'locus' of the center of gravity for the case that thequay is not present, all other data being the same. It is seen that for that case the locus is again almost circular.
In Figure 17 though Figure 19 we compare the forces and moment on the moored
tanker of the previous case (alongside a quay) with the same run without the effect of the quay, i.e. the open water case. The computations have been carried out using the double-body model. The results show that the presence of the quay increasesthe surge force by about 80% and reduces by about 60% the sway force and the yaw moment. 'Clearly, the passing forces on a ship' moored in open water are not a good measure for
the forces'ona ship mooredalongside a quay
'The next case concerns the same vessels but now the harbour geometry consists of'a '10,000 m long canal of 600 rn width with a dock to one side half-way the length of
Surge torce
Figure ¡3: Surge force alongside quay. Figure 14: Sway force alongside quay.
Locrl of Center of Orevtiy
Yawmriment '1000 Um. tiri - bou..bedy - - FÍ-oiirIwe 1500
Figure 15: Yaw moment alongside quay. Figure 16: Locus of center of gravity.
Sur. Iwo,
Figure 17: Surge force open/alongside. Figure 18: Sway force open/alongside.
p i
-X
r - - Open writer - Allgsideqray .10 .5 0 5 10 &119,orm Swoy bree 400 -- -- Free--melee. -400 400 800 lOCO time er, 'sao 800 -400 - - Free-metric,L
.400 4000 lOCO 1800 2000 timen, B Eio
-Gloo loo loo o .iòóo -2000 swu 50 1000 tini.i I
Figure 21': Surge force in dock
Vow moment - Di.bbody - - Frei Irres, --60 0000 0 SWOy reste - Ube.bod, - - ROD-Wend
Figure 22: 'Sway force in dock
Looms of Centec olGravSy
Figure 23: Yaw moment in dock Figure 24: Locus of center of gravity.
free-surface method the passing ship generates waves due to the discontinuities in 'the canal geometry. These waves propagate into the dock effectively carrying the impuls imparted by the passing ship to the moored vessel with very little decay.
In Figure 25 the wave elevation on thecenterline of the dock abreast of the half length of the tanker and the heave motions of the tanker areshown., As can be seen thewaves
have long periOds associated with seiches and the vessel, large though it is responds with 'almost the same vertical motions
The last case concerns a real.-life situation encountered in the portof Rotterdam, The Netherlands. To the south of the main sea-port there is a 6 km long and 110 m wide
inland waterway known as the Hartelkanaal. This canal carries inland traffic taking
cargo from ocean-going vessels to 'the hinterland. The traffic consists, among others, of pusher-bargecombinations with 4 barges in a 2 by 2 arrangement. The' deadweight of thetota1 combinationis approx. 12000 tons. In the'late 70's it was noticed that at the location of the lock at the end of the canal, see Figure 26, right, unexpected waterlevel
rises were experienced without apparent cause. This rise in the waterlevel resulted in damage to mooring systems of vessels waiting to enter the lOck. A monitoring
campaign was set up through which traffic entering the canal at the western end (left
'I I - - Fne,.iwfsceDntibls.bod 2009 4000 Orne ms 2ß o 25 2300 4000 time is e 2 -1 -2 0 2 4 sesgein m
0.04 02 0 E .ft02 0.04 .0.00 0 Wave . Heave
- - Wave ab,ea ofter*e,
- HeCve
4000
Figure 25: Wave elevation and heave in Figure 26: Hartel canal.
dock.
in Figure26) wastrackedand, at the same time waterlevels were monitored in thebend
of the canal and at the lock. See ref.[2]. It was found that large barge combinations
entering the canal set up a wave of translation, or solitary wave, on the combination entering the canal at the western end., By the time the combination neared the bend, thesolitary wave arrived at the lock. Waterlevel rises of upto 40-60 cm were recorded
fórbarge speedsof4-5 rn/s.
We have recreated the case of a barge combination entering the canal at 4 rn/s at the
western end. As no exact details of the vessels tracked in the full-scale measuring campaign were available, standard dimensions were used. The 4 barges ina 2-by-2 arrangement are modeled as a single barge with following main dimensions:
Vessel displacement m3 13340
Length between pp m 153.00
Breadth m 2280
In the C mputations have not includedthe possibility for thebarges tosail throughthe bend in: the canal, consequently, the barges proceeds into the canal and slow down to stop in the bend. Since the observed generation of the solitary wave took place in the first section of the canal, before thebend, we expect this toibe thecase inthecomputa-tions also. Theinitial and final posiinthecomputa-tionsof the barges are shown in Figure 26. Results of the computions, which have been carried out using the free-surface code only, are
the wave elevation records at the bend and at the lock. These records are shown in
Figure 27.
Figure 27 shows that shortly after the barges enter the canal' (at 450 s), a single wave peak followed by a shallow trough passes the bend moving at thecritical velocity and arrivesat the lock. At the lock the wave elevation isdoubled (full reflection against the closed lock gate), and the wave then proceeds back dOwn the canal and again passes
0.4
0.2
o
.0.2
Wave elevetfon In HaeIkanaar
Wave height No. of cases
The case investigated here involved the largest barge combination. During the full
scale measuring campaign themaxirnum recorded speed of one of thebarge combina-tions amounted to 4.5 mIs. The computed maximum wave elevation at the lock close to 40 cm for a speed of 4 rn/s fits in very well with the second highest class of wave elevations measured in full scale.
These results beg some discussion since this type of solitary wave is generally
consid-ered to be associated with a non-linear wave description i.e. the Korteweg-de Vries equation. See, for instance, ref. [.10]. The results shown here have been obtained
using linear potential theory only. Why then the singlesolitary wave withalmost
con-stant shape? The explanation lies in the fact that the wave is built up from a linear
superposition of a large number of, in this case 307, frequency components of which the maximum frequency is 0.15 r/s. The waterdepth in the canal is 5.7 m.. This means
that the major part of the waves are shallow water waves travelling at speeds very close to thecritical velocitybeing where g is theacceleration of gravity and h the
waterdepth. In this case, even though linear dispersion applies, it's effects are small
over the length of the canal and the wave maintains it's initial shape very well.
- - tiv. at bend - Wav.attod, -.-,
'.-\_2'--.. ,
lOto2Ocm 9 2Oto3Ocm 13 3Oto4Ocm 3 60cm 1 500 !000 1500 2000 Urnetia sFigure 27: Wave elevations in canal.
the bend with approximately the same elevation as seen initially. The wave elevation at the lock corresponds well with the values measured in the full scale campaign for theship'sspeed of 4 rn/s. See ref. [2] Unfortunately, no time records of the measured wave elevations have been included in this reference. For a number of recorded cases
(passing barge combinations) the range of the maximum wave elevation at the lock
4. Conclusions
Wehave presented two methods for the computation ofpassing ship effects on moored vessels i.e. a double-body flow model similarto that first applied by Korsmeyer et al [4] and a new method based on the mixed application of double-body flow and linear diffraction computations including. free-surfaceeffectsfirst introducedby Pinksterand Naaijen [7]. Botharebasedon the applicationiof3-d.potential flow methods. The flow equations aresolved using azero-order panel method.
The new method has been validated based on compaiison of results of computations
with results of model tests presented by Remery for the case of a ship moored in
open water. No model test results for more restricted waterways are at present
avail-able so the influence of free-surface effects, which manifest themselves most when
the harbour/fairway geometry becomes complex, could only be investigated using the ñumerical models.
Based on comparison of results using both models the following conclusions can be drawn:
s Free-surface effects are negligible for the case of a vessel moored in open water.
This suggests that, for instance, for vessels moored to open jetty's which are not too close to the shore, double-body flow computations are adequate for the prediction of passing ship forces.
It has been shown that forthecase of a vessel iiiooredto a long, vertical quay wall,
that the new model again agrees well with the double-body model. Care was taken to avoid transient effects in the free-surface method in order to comply as much as
possible with the assumptions of a long, straight quay and a passing vessel travelling at constant speed over a long distancealong thequay.
It has been demonstrated that if a vessel is moored alongside a vertical quay, the
passing ship forces in surge are approximately 80% larger and the sway forceand yaw moment 60% smaller than is the case if the moored ship is in open water. Predictions
of mooring forcesofvessels moored toa quay should not be basedon open waterdata
of passing ship forces.
The influence of free-surfaceeffects on the forceson a ship moored in a dock to the side of a fairway can be very large. In such cases, the double-body flow, in Which the influence'of a passing shipreduces with IIR, R being the:distancebetween mooredand passing ship, predicts relatively low forces. Free-surface effects manifest themselves as seiches, or long waves, set up by thepassing vessel at the entrance to the dock and which then progressi Without loss of energy into the dock where they exert forces and moments on the moored vessel.
Using the new computational procedure including free-surface effects is has been
shown that predictions can also be made of the formation of solitary waves due to
geom-etry of the fairway. Computed wave elevations compared favourably with full scale measurements.
Initial indications based on the resùlts of computations, suggest that free-surface
effects should be considered in cases with complex harbour geometry, however,
val-idation of computations of free-surface effects through comparison with results of
model tests should take place before final conclusions can be drawn in this respect.
References
National Transportation Safety Board, Explosion and Fire aboard the U.S. Tank-ship Jupiter, Bay City, Michigan, September 16, 1990, Marine Accident Report PB9 1-916404, NSTB/MAR-9 1/04, Adopted Oct. 29, 1991.
Rijkswaterstaat, Adviesdienst voor Verkeer en Vervoer, Onderzoek
Trans-latiegolvenop Hartelkanaal, Nota S 78.29, Dordrecht, 1979.
King, G.W, Unsteady Hydrodynamic Interactions Between Ships, Journal of
Ship Research, Vol. 21, No. 3, Sept. l977
Korsmeyer, F.T., Lee C.-H. and Newrnan,JN., Computation of Ship Interaction Forces in Restricted Waters, Journal of Ship Research, Vol. 37, No. 4, pp 298-306, 1993.
Grue, J. and Biberg, D., Wave Forces on Marine Structures with small speed in water of restricted depth, Applied Ocean Research 15, pp 121-135, 1993.
Remery, G.F.M., Mooring Forces induced by Passing Ships, Paper No. 2066,
Proceedings of the 6th Offshore Technology Conference, Houston, Texas, 1974.
Pinkster, J.A. and Naaijen, P., Predicting the Effect of Passing Ships, 18th
In-ternational Workshop on Water Waves and Floating Bodies, Le Croisic, France, 2003.
Pinkster, J.A., Hydrodynamic Interaction Effects in Waves, ISOPE'95, The
Hague, 1995.
Newman, J.N., Algorithms for the Free-surface Green Function, Journal of
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