2nd International Conference on SJiip Manoeuvring in Sliallow and Confined Water: Ship to Sliip Interaction
SQUAT OF SHIPS SAILING IN A NON C E N T E R E D T R A C K IN A CANAL
H J de K o n i n g Gans, Delft University o f Technology, The Netherlands S U M M A R Y
Squat is a serious problem when very large container ships are entering harbours w i t h small underkeel margins. The squat effects are that the ship acquires sinkage and t r i m . Due to this sinkage and trim the keel clearance decreases drastically. The distance between bottom and ship becomes very small and measures must be taken to avoid contact between the ship and the bottom.
Also when the ships are not sailing in the centre o f the canal, the squat effects become more serious. The f l o w around the ship is not symmetrical anymore, and also the gap between the wall and the ship becomes smaller and higher return flows are expected. This w i l l cause extra forces to act on the ship and as a result, the ship w i l l suffer extra squat-effects.
This study looks at several sailing tracks at the centre and parallel o f the centre line o f the port. The f l o w calculations are carried out w i t h a three-dimensional potential f l o w model. For this model the wetted hull geometry has only to be determined o f the underwater body (wetted hull) in still water conditions. From these calculations the pressures on the wetted hull are determined and by integrating the pressures, the forces are determined. From each track the forces are determined and the trim and sinkage are calculated. From these results, it appears that, when the ship sails more closely to the w a l l the forces w i l l increase drastically.
N O M E N C L A T U R E B Breadth o f t h e ship, (tn) FJ 1 <J<3 Force in J direction (N) Fj 4<J<6 Moment in j direction (Nm) Fs Sinkage force amidships (N) Fs Trimming moment amidships {Nm) g Acceleration o f the gravitation {ms'^) it Initial water depth (/«)
K Keel clearance or minimum distance between ship and bottom (/n)
L Length o f the ship (in) n Normal vector ( )
p Pressure (on ship surface) in water {N) s Sinkage in amidships (positive to beneath) {m) T Draught o f the ship (/»)
/ Trim angle (positive ahead) {rad) U Ship Speed {ms')
u Longitudinal velocity component o f a water particle {ms'')
V Cross velocity component o f a water particle {ms'')
w Vertical velocity component o f a water particle {ms'')
r Distance between two points {m)
X Local coordinate in longitudinal direction (w) y Local coordinate in cross direction (77?) z Local coordinate in vertical direction {m) tp Potential function {m^/s)
ju Dipole strength {m^/s) a Source strength (tn/s)
C Change o f local water level (positive above) {m) p Specific weight o f water {I<gm'^)
Q Surface area o f wetted h u l l {m^)
1 I N T R O D U C T I O N
Recently, the Rijkswaterstaat' got a message that a b i g inland vessel was sailing close and parallel to the quay and this ship was not able to sail to the centre o f the canal. The only solution was to stop the main engines and to manoeuvre the ship w i t h l o w speed to the centre o f the canal. When it arrived there, the l i i l l speed manoeuvre could be continued.
Apparently side forces occur, when ships are sailing close to quays. These forces are so big that a ship is not able to react f o r a safe sailing through the canals. What happens is the f o l l o w i n g . The ship is controlled w i t h a rate o f turn feedback indicator. This steering controller is very w e l l able to keep a ship on course, but it is not able to control i n cross direction (and it time derivatives). When the ship has an initial offset, the ship experiences a force i n the direction o f the quay. Due to this force, the ship w i l l accelerate and move to the quay. A n d when the ship becomes closer to the quay the (side) forces become higher. The controller w i l l cause that the ship w i l l not get a d r i f t angle, so it is not possible to generate a force on the ship i n the centre direction o f the canal. The result is, that the ship w i l l sail parallel and closer to the quay. A n d when the captain does not pay attention to this effect, the ship w i l l touch the quay almost parallel.
From the above phrase, it appears that side forces occur when ships are not sailing in the centre o f a canal.
Another point o f view is that the most formulae's, to predict the squat (sinkage and/or t r i m ) (see [ 1 ] , [17] and [19]), are only valid in the centre o f the canal. I t is expected that the squat w i l l increase when the ship is not sailing in the centre o f the canal. To get an impression to predict squat effects, this study has been
2nd Intemational Conference on Ship Manoeuvring in Shallow and Confined Water: Ship to Ship Interaction
set up. In previous research it is already proven that panel methods are a suitable tool to predict the sinkage and trim (see [ 9 ] , [10] and [11]). To make a proper investigation in this research, a panel method is used.
2 C A L C U L A T I O N M E T H O D
2.1 P A N E L M E T H O D S , T H E T H R E E D I M E N S I O N A L M E T H O D
In the last part o f the previous century numerical methods have been developed to calculate the potential flow, w i t h or without wave pattern around ship hulls. The advantage o f numerical methods is that the velocities and pressures can be calculated at each point o f the wetted surface o f the ship hull as well as at the free surface. Also the forces and moments can be determined by integrating the pressure w i t h respect to the wetted hull. So more and new insights concerning the behavior o f the f l o w can be analyzed. The tests can be carried out with or without free surfaces effects. When the geometry or f l o w direction is changed a quick calculation can be made in order to gain more insight regarding the characteristics o f the f l o w . A t the T U D e l f t a numerical method based program was developed. This program is based on a panel method using a Dirichlet boundary condition. The panels are placed on the wetted hull surface and on the free surface around the ship. The program can predict the double body f l o w when panels are only placed on the wetted hull. This program can also be used f o r wave pattern calculations, but as it w i l l be mentioned i n section 2.6, but at l o w Froude (based on the ship length) wave pattern calculations are not important f o r problems concerning sinkage and trim. The model is based on a potential f l o w . Some important properties and characteristics o f the potential theory are discussed below.
For the simulation o f the f l o w around a floating object a simplified flow model is used. One o f them is the potential flow model. This model is a theoretical flow model and it has some important characteristics, which can be used f o r calculations o f the flow. One o f these characteristics is, that an integral method can be used f o r simulating the flow. N o w some o f the characteristics thereof w i l l be discussed. The potential flow is assumed to simulate an incompressible and inviscid flow around a proflle or body. This means that only mass inertia forces are simulated and no drag can occur. And also this means that there w i l l be no vorticity i n the flow. Due to the fact that the flow is incompressible, the flow w i l l be divergence free. The means that i n the flow no material w i l l be created nor destroyed and is called the equation o f conservation o f mass. N o w the potential flow can be described as a solution o f the Laplace equation:
a^(5 a^(D a ^ o „
A<5 = — - + — - + ^ = 0 (1) dy^ dz^
This is a homogeneous and linear differential equation and so the superimposing property can be used. W i t h this
propeity, it is possible to transform the Laplace equation into the Fredholm's integral equation with help o f Green's theorem.
2.2 I N T E G R A L E Q U A T I O N S
For solving the potential, the Fredholm integral equations o f a second kind are used. On the surface o f the body a source and a dipole layer w i l l be placed. Thus the following integral equation is used, w i t h the Greens function, which represents physical sources and dipoles:
rp{x) = f f { a { X ) + / / ( " ^ ' " / ^ ^ ^ ^ (2)
In which /• is the distance between an arbitrary point and a point at the surface Q. The surface Q is divided into the wetted surface o f the double body QB and the canal wall and bottom Qc- To solve the integral equation the inner Dirichlet boundary condition is used. The source strength a at the fixed wetted surface QB and canal wall and bottom ö c t h e n is:
a = ^ = -<U^-n> (3) dn
For simulating the flow with a potential flow solution a number o f boundary conditions have to be obeyed. The boundary conditions have to be obtained at the wetted surface o f the ship body, at the free surface and far away in front o f the ship the wave height and the derivatives thereof w i l l be zero. When no free surface flow is obtained, all the boundary conditions can be applied as no leakage condition or kinematic boundary condition. The flow at the solid body QB and canal wall and bottom Qc w i l l be tangential to the surface. This means that there is no velocity component i n normal direction. This can be written as an inner product:
< V O - « ^ > = 0 (4) By making use o f the potential j u m p relation o f a dipole
layer and o f the choice that the inner potential g)=0 , the perturbation potential can be determined at the outer surface according to the so-called j u m p relation:
(p{p&a)
= -/uiP) (5) According to this equation the potential at QB is known. The first (partial) derivative o f the potential i n any direction delivers the velocity in that direction. So, by taking the first spatial partial derivatives o f the potential along the wetted hull, the velocities are obtained on the surface o f the body. The fiuid velocity at a control point is:2nd International Conference on Ship Manoeuvring in Shallow and Confined Water: Ship to Ship Interaction
2.3 PRESSURES A N D FORCES
The pressure at any particular point can be determined with the Bernouilli equation:
, - _ 1
p = p <v - v > +C = p <v - v > +^ pUt (7) The constant is determined at 'infinity' fiir in front o f the ship, where the water is in rest and so the perturbation velocities and perturbation potentials are 0. ( C = / 4 / j f / o o ) The velocities in this equation (7) are determined from equation (6) by taking the gradient o f the potenfial. B y integrating the pressures from equation (7) over the ship surface the forces Fi to F j are determined:
F = -pndQ. For the first 3 components (8)
The moments on the ship Mi.Mf^ F^ ..F^ are determined by using the cross product o f the normal vectors and the distance vector f r o m the ship centre and these results are integrated over the ship surface Q:
M - -pri X rdO. For the last 3 components (9) n
To find the sinkage and t r i m , the equations (12) and (13) can be used by filling i n the values o f F^ and Fs respectively.
2.4 SINICAGE A N D T R I M
The sinkage and trim can be obtained by using Archimedes' law. When the sinkage is defined as s (positive downwards) and the trim is defmed as t (positive ahead), the equilibrium according to Archimedes' law for a trim and sinkage ship is:
pgj (s + xt)B{x)dx = spg ƒ B{x)dx + tpg j xB{x)dx (10) • pg{A^,.s + S j ) = ^F^
pg \(s + xt)xB{x)d\ = spg J xB(x)d\ + tpg J x^B(x)d\ = pgiS^.s + I^.t) = F,
I n this equation the f o l l o w i n g known quantities appear: A»:. the water area or zero order area, S/. the static moment or first order area and I/, the moment o f inertia or second order area o f the water plane defined f r o m amidships. Substituting these parameters in equation (10), the f o l l o w i n g matrix equation is obtained:
(A.
' A
[s,
f j
V ^ 5J
(11)This matrix equation can be solved easily, the results are:
A n d
t =
-pg{AJ^,-Sj)
pg{AJ^,-Sf.)
For the sinkage (12)
For the trim (13)
The forces Fj and F 5 are already obtained by equafions (8) and (9). The keel clearance is obtained by the subtracting the draught T o f the ship and the influence o f the sinkage and trim f r o m the water depth h: (See also Figure 1):
K = h-T- (14)
For the keel clearance it does not matter i f the trim is by head or by stern, when the origin o f the coordinate system o f the ship is defined amidships. B y the same amount o f trim (ahead or astern) one part o f the keel reaches the same distance closer to the bottom.
OriginaJ position ship
Still water level ^ + xt + s
Position of the ship due to squat effects
Figure 1 N e w situation when a ship sails in squat condifions
When a heel angle is taken into account, then this heel angle can be calculated as follows:
<P • (15)
pgS/GM
So, when a heel angle is present, the minimum value between the ship bottom and canal bottom has to be found. I t is more practical to introduce a frame box around the under water ship and this frame box has the dimension o f the length, breadth and draft. N o w the virtual sinkage at one o f the corner points o f the frame can be determined. I n this case the maximum total sinkage (s,„a^ is:
2.5
max
2
9P A N E L M E T H O D S FOR S Q U A T C A L C U L A T I O N S
(16)
For free surface calculations, including the wave pattern, the speed o f the ship has to be considerable. The most wave pattern prediction programs require a panel density o f 12 panels per wavelength and for an accurate calculation the programs require even a density o f 20
Ind International Conference on Ship Manoeuvring in Shallow and Confined Water: Ship to Ship Interaction
panels. When a ship sails w i t h a speed o f 10 knots = 5.144»;A' the generated wavelength is:
g
This means, that the panel length at the free surface should have a length between 1 .Om to 2.0m. For a stable and a realistic wave pattern calculation the free surface has to be panelised almost a half o f the ship length in front o f the ship and a ship length aft o f the ship. For a ship o f a length o f 300m or more at least 500 panels has to be generated i n longitudinal direction. For a more accurate calculation, the number o f panels should be even higher than 1000 panels. Also in cross direction the panel width should be the same dimension as the panel length. So, a lot o f panels in width direction have to be generated too. The panel distribution on the ship hull should have almost the same measurements as the free surface panels. This means, that an enormous number o f panels has to be generated (±10®). Further the matrix is a f u l l matrix and it has to be stored inside the computer. This requires a lot o f computer memoiy, which is not available. Also, due to the large amount o f numbers the inversion process w i l l deliver poor results, due to a bad conditioned matrix (, the von Neumann condition o f a matrix is also linear with the number o f rows.) From this point o f view, it is expected that no reliable or unstable results may occur and it is not recommendable to use a free surface calculation.
Fortunately with this very low speed o f the ship the wave effects on squat effects are negligible. The wave influence i n vertical direction reduces very rapidly and at one wave length under the free surface the influence is approximately 0.2% o f t h e effect at the free surface. The bottom o f the ship does not experience much o f the disturbed pressure o f the generated K e l v i n waves. Also the amplitude o f the wave is very low. So, at low speeds o f the container ships i n a harbour, the free surface waves or K e l v i n waves do not influence the squat. This means that when a panel method is used, the free surfaces do not have to be modelled.
2.6 A D A P T A T I O N OF T H E P A N E L M E T H O D FOR S H A L L O W W A T E R
The above methods describe, that the sinkage is consists o f a Froude depth number dependent part and a geometrical or shape o f the ship hull. The squat can be calculated according to:
s = f{,F„)g(Geom) (17) For the linear squat calculations, when a panel method is used, the same principle is used. When only the panel method in the original case is used, the surfaces o f the bodies are rigid. Furthermore the free surface is removed and the calculations are carried out by a mirrored body model, where the hull and the bottom are mirrored in the free surface. The calculated pressures are proportional to the square o f the velocity. From this, the forces, moments, sinkage and t r i m are also proportional to the square o f the velocity:
p,F,M,s,t ~v^ ~F,^ (18)
However, by using the panel method, the shallow water equation is not built i n . Tuck (see [19]) has derived, that for shallow water problems, the potential equation has to f u l f i l l the shallow water hydrodynamics. From this shallow water hydrodynamics equation the calculated pressures, forces and moments are proportional to:
F^
p , F , M , S , t — i = J ^ (19)
3 T H E S Q U A T R E S U L T S
3.1 T H E D I M E N S I O N OF T H E C O N T A I N E R VESSELS
The calculations have been carried out f o r one type o f container ship, one canal depths and four different offsets o f the center o f the canal. The type o f containers ship is the so called ' M E G A JUMBO'. The canal depth is 19.65m and the initial keel clearance (this is the keel clearance when the ship is in rest) is 2.65m. The
dimensions and the specific ship parameters are shown i n table I .
Ship D i m . M E G A
J U M B O
Container Cap. [TEU] 12500
Length o.a. [m] 382.0 Length p.p. Lp„
['"]
364.9 Breadth B['"]
57.0 Depth H['"]
30.0 Draught T['"]
17.0 Displacement V[»'']
242911 Block coef. Cb[]
0.6870 Slenderness c o e f A =[]
5.848Loc. O f center o f buoyancy [w]
[%]
-5.65 (=-1.55)
Waterline area^^,,. W] 16902
Waterline area coef. CWL
[]
0.8126Loc. o f waterl. cent. Xj^z,
['"]
[%]
-16.44 (=-4.51) Static moment o f W . L . ' Sy ['A -277919
M o m . o f inertia o f W.L.^ ƒ,, 13818744
Table 1 Dimensions and specific parameters o f the tested container ship.
The dimensions o f the canal are 600/;; (width) and 19.65;;; (depth). The simulations are carried out at the center o f the canal and at three different offsets. The offsets are respectively 25%, 50% and 75% o f t h e h a l f
2nd International Conference on Ship Manoeuvring in Shallow and Conf ned Water: Ship to Ship Interaction
width o f the canal. The corresponding offsets in meters are respectively 0, 75, 150 and 225 m. A l l the simulations are can-ied out with a unit speed o f 1 m 'and without a drift angle.
To obtain the real forces and sinkage and trim can be calculated as follows. The real values are obtained by using the results at the unity speed. These values have to be muhiplied with the square o f the real velocity. According to these multiplications the linear results are obtained. When the shallow water equation (jii'e) correction is included, the linear (///?) results have to be multiplied again w i t h the so called shallow water correction:
^ . , . = - | ^ = (20)
3.2 T H E S Q U A T RESULTS OF T H E P A N E L M E T H O D S
3.2.(a) The pressure distribution
The resuhs o f the panel method are presented in figure 2 to figure 9. I n the first four figures (2 to 5) the velocities along the hull and canal walls are shown as w e l l as the pressure. I n the last four figures (6 to 9) only the
pressures at the wetted hull o f ship are shown. Looking at the pressures i n these figures already some remarks can be made and insight can be obtained. From these figures, it is obvious that the pressures become less when the ship sails more i n the vicinity o f the quay. Due to these lower pressures, it is expected that a larger sinkage force and trim moment w i l l occur and so, the ship w i l l have a sinkage and t r i m . This sinkage and trim w i l l be larger when the ship is sailing closer to the quay.
Figure 2 The pressure and velocity distribution at the ship and bottom at a offset o f y = Om.
7 1 500 r 450 400 350 300 250 200 150 100 450 400 350 300 250 200 150 100 -50 -100 -150 -200 -250 -300 -350 -400 -450 -500
Figure 3 The pressure and velocity distribution at the ship and bottom at a offset of;^ = 75m.
Figure 4 The pressure and velocity distribution at the ship and bottom at a offset o f > ' = 150w.
The most important calculated variables are presented in Table2. I n this table the results are obtained at the unity speed. y (m) 0 75 150 225 F2(kN) 0.00 8.571 30.82 135.5 F3 (h'lN) -2.246 -2.280 -2.438 -3.111 F., (A'INm) 0.00 -0.1189 -0.4224 -1.853 F, (A'INm) 21.06 21.39 22.67 25.93 s (lO 'm) 13.49 13.69 14.64 18.72 t ( I f f ' ' rad) 11.88 12.06 13.04 18.89 (p ( I f f ' rad) -0.02 -9.793 -34.77 -152.6 S f ( I f f ' m ) 15.65 15.89 17.02 22.16 Ss (lO-'m) 11.32 11.49 12.26 15.27 ( I f f ' m ) 0.00 0.2791 0.991 4.348 Smax ( I f f ^ t t t ) 15.65 16.17 18.01 26.51 Table2 Squat results at unity velocity
2nd International Conference on Ship Manoeuvring in Shallow and Confined Water: Ship to Ship Interaction
Figure 5 Tiie pressure and velocity distribution at tiie ship and bottom at a offset o f ; ' = 225«;.
pr
•
500 L . 450 400 350 300 250 200 150 100 50 0 -50 -100 f— -150 1— -200 \— -250—
-300 -350•
-400 -450•
-500Figure 6 and 7 The pressure distribution at the wetted hull o f the ship at a offset o f j = Ow (left) and j = 75m (right) respectively.
From the resuhs presented in Table2, ft is obvious, that when the ship is sailing more in the vicinity o f the quay that all the forces and moments increases. N o t only the vertical force is increasing, but also a side force {F2) occurs. This force becomes greater, when the ship sails in the vicinity o f the quay. Also the moments are increasing and when the ship sails closer to quay a heel moment occurs as well.
Figure 8 and 9 The pressure distribution at the wetted hull o f the ship at a offset of_y = 150;w (left) a n d j ' = 225;h (right) respectively.
From the results, shown i n Table2, h is possible to present the sinkage as function o f the ship speed. The presented sinkage is calculated amidships and at the place where the frame box^ o f the underwater ship has it highest sinkage. The sinkage, presented in figure 10 and figure 12, is proportional to the square o f the velocity. The sinkage, presented i n figure 11 and
13
Highest sinkage of frame box acconjing to sliallow waterequation
2 3 4 Velocity [m/s]
Figure 13, is according to the shallow water equation.
The frame box is a fictive rectangular box around the ship and has the dimension ofthe length L, breadth B and draft T
2nd Intemational Conference on Ship Manoeuvring in Shallow and Confined Water: Ship to Ship Interaction
Highest sinloge of framefwx
Velocity [m/s]
Figure 10 The sinkage amidships as function o f the velocity at several offsets according to the linear equation.
Sinloge; shaliow water equation
Velocity [m/s]
Figure 11 The sinkage amidships as function o f the velocity at several offsets according to the shallow water equation.
Velocity [m/s]
Figure 12 The sinkage at the corner o f the frame box as function o f the velocity at several offsets according to the linear equation.
From these figures (10 to 13), it appears that the sinkage according to the shallow water equation is a slightly more than according to the square velocity.
In this case the Froude depth number is not very high as well (The maximum Froude number is Fj, = 0.428 at 6 ms' = 11.66 hiots) and the correction o f the shallow water equation is a factor 1.1 (=1/V(1- f ) / ) ) .
The figures 14 (amidships) and 15 (frame box) present the sinkage as function o f the offset o f the track f r o m the center o f the canal. The ship speed i n the presented figures is 5 ms'' = 9.72 knots, which is a realistic velocity in a port environment. From these last two figures, i t appears that the squat increases when the ship i n more close to the quay. However the sinkage increases drastically when the ship is in the proximity o f the quay.
0
Highest sinl<age of framebox according to shallow water equation
0.1 0.2 0.3 : ^ 0 . 4 c ; . c . a 0.5 ai | 0 . 6 ^ ^ 0 . 7 0.8 0.9 -. c -. a 0.5 ai | 0 . 6 ^ ^ 0 . 7 0.8 0.9 y = Om y = 76m y=150m y=225m 1 I 1 1 1 1 2 3 4 5 Velocity [m/s] 6
Figure 13 The sinkage at the corner o f the frame box as function o f the velocity at several offsets according to the shallow water equation.
2nd Internalional Conference on Ship Manoeuvring in Shallow and Confined Water: Ship to Ship Interaction 0 0.05
r
0.1-
Sinkage amidships 0.15-E"
0.2 (U1
0.3 0.36-Sinkage according to linear squat Sinkage according to stiallowwater equation
E"
0.2 (U1
0.3 0.36 0.4 0.45 0.5^-. 1 1
1 . i
1 1 1 . ^~"~77-,,
0.45 0.5^ 50 100 160 200Off set of center of c a n a l [m]
Figure 14 The sinkage amidships as o f function o f the offset at a velocity o f 5m/s
Not only an extra sinkage, t r i m and heeling occur when the ship is not sailing along the center track, but also a side force {F2) and a yawing moment appear. The side force is presented in figure (16). The yaw moment is very dependent o f the ship geometiy and this is not presented here. The side force (F;) as function o f the offset o f center o f the canal is presented i n figure. I n this figure the ship is 5 m " ' a n d this is a realistic situation.
From this figure (16), it is obvious, that the side force increases drastically, when the ship sails more i n the vicinity o f the quay. Due to this force, the ship w i l l accelerate to the quay and when no opposite forces are introduced, the ship w i l l really move to the quay. To remain on a stable course, opposite forces are needed. Opposite forces can be obtained by wind forces, tugs or by introducing a drift angle, such that the bow points to the center o f t h e canal. H o w closer the ship is in the vicinity o f the quay, how larger the drift angle should be.
Op
0.05 r S Inkage deepest point of framebox
0.1 f 0.15 I
0.2 i Sinkage according to linear squat
0 25 i- Sinkage according to stiallowwater equation
ra ° '' '? ' •&45 r
~—
^^^^^rzi;;;^;;—^
"5 0.5 r ~ X X 0.65 I-0.6 r 0.66 \ \ 0.7 - \ 0.75 '-O g E j— I — I —I — I —1 —I — I — I — I — I— I —,—1 — L _ i —1 — I —I — I — 1— 1 _ 0 50 100 160 200Off set of center of c a n a l [m]
Figure 15 The sinkage at the deepest corner o f the frame box as o f function o f the offset at a velocity o f 5m/s
4 r
Side force at 5 m/s
3.6 3
-I ' '
-linear side force acc. to stiallow water eq.
forc e r
ƒ
Cl S 1.5 (0 1 r 0.5 ^ : T Ï . . . . 1 . . . . 1 . . . . 1 . . °( 60 100 160 Off s e t [m] 200Figure 16 Side force at a ship speed o f 5m/s
During the simulation tests no drift is taken into account. From previous research (see [ I I ] ) , it appears, that f o r ships sailing under a drift angle, the squat effects increases as well. From this research, it appears that the extra sinkage is o f t h e same order as the sinkage at the center o f the canal. However, it is unknown, when the ship sails i n the vicinity o f the quay, how large the (extra) sinkage w i l l be. when the simulation are carried w i t h a drift angle.
4 S O M E R E M A R K S A N D D I S C U S S I O N S
The simulated tests are caiTied out in a potential fiow model. This model simulates only the inertia forces o f water, while the viscous forces are not taken into account. H o w important the viscous influences are, is not researched, but comparing squat results fi'om tank tests, the viscous forces are not quite important (see [ 7 ] ) .
In this research no propeller interaction is taken into account. When a propeller is used, this propeller w i l l suck the water under the aft ship and lower pressure w i l l occur. The result o f this is, that an extra t r i m moment w i l l occur and that the ship w i l l be trimmed more to the stern.
5 R E C O M M E N D A T I O N S
• Equations, which predict the squat, have to be adapted for ships, which are not sailing at the centre o f the canal.
• N e w calculations have to be carried out w i t h drift angles. These calculations can also be done w i t h a panel method (or boundary element method). Two types o f calculations can be distinguished, with or without l i f t effects. When l i f t effects are applied a vortex sheet behind the ship has to be created as well and a Kutta
2nd International Conference on Ship Manoeuvring in Shallow and Confined Water: Ship to Ship Interaedon
condition has to be appHed at the end o f the centre plane o f the ship.
• More simulations with other type o f ships have to be carried out to give more insights o f squat effects, when ships are not moving in the centre o f the canal.
• To validate these squat results, towing tests have to be carried out.
6 C O N C L U S I O N S
e Panel Methods give an indication to predict
squat, even when ships sails i n the vicinity o f the quay. However the results should have to validate w i t h experiments.
• From the calculations, h appears that forces increase when ships sail closer to the quay. The forces grow drastically when the ship sails i n the vicinity o f the quay.
• Also the squat effects (sinkage and trim) become larger. This means, that equations used to predict the squat, are only valid f o r ship sailing at the centre o f the canal.
e Beside the trim and sinkage, also a heel angle
occurs when the ship sails close to the quay. 7 R E F E R E N C E S
[1] Barrass, C B . "Ship Squat - A Reply", The Naval Architect, November 1981
[2] Beck, R.F., "Forces and Moments on a Ship M o v i n g in a Shallow Channel", Journal o f Ship research. Volume 2 1 , N o 21 June 1977, pp 107-119
[3] Breh, S.R., "The Potential o f a Rankine Source between Parallel Planes and i n a Rectangular Cylinder", Journal o f Engineering Mathematics 25 pp.151-163, Kluwer Academic Publishers, Printed in the Netherlands, 1991
[4] F l ü g g e G. & Uliczka, K . , "Fahrverhahen grosser Containerschiffe in extrem flachem Wasser, Das dynamische Fahrverhahen und die Wechselwirkungen mit der Fahrrinennsohle von sehr grossen
Containershiffen unter extremen
Flachwasserbedingungen.", Hansa-Schiffahrt-Schiffbau-Hafen-138.Jahrgang-2001-Nr 12
[5] Hermans, A.J., "Ship Manoeuvring and
Hydrodynamic Forces Acting on Ships in Confined Waters", Proceeding o f Symposium on Aspects o f Navigability, D e l f t , 1978
[6] Katz, J. & Plotkin, A . , "Low-speed aerodynamics f r o m w i n g theory to panel method", I S B N 0-07-100876¬ 4, M c G r a w - H i l l , Inc., Singapore, 1991
[7] Koning Gans, H.J. de, "Squat effects o f very large container ships sailing in a harbor environment". Report No.I407-O,Laboratory o f Ship Hydromechanics, T U D e l f t ( D e l f t University o f Technology) and Port Research centre Rotterdam-Delft Publications , November 2004, D e l f t , I S B N 90-5638-134-2
[8] Koning Gans, H.J. de, "Squat Results f r o m Calculations o f Panel Methods", Report N o . l 4 0 8 - O , Laboratoiy o f Ship Hydromechanics, T U Delft (Delft University o f Technology) and Port Research centre Rotterdam-Delft Publications, November 2004, D e l f t , I S B N 90-5638-135-0
[9] Koning Gans, H.J. de, "Squat Effects o f very Large Container Ships Sailing in a Harbor environment", 'International Maritime-Port Technology and
development Conference 2005, Rotterdam', September 2005, Rotterdam, I S B N 90-80989-21-5 (old) I S B N 978¬ 90-80989-21-4 (new)
[10] Koning Gans, H.J. de, " A Method to Predict Forces on Passing Ships under D r i f t " , 9th International
Conference in Numerical Ship Hydrodynamics, August 2007, A n n Harbor
[11] Koning Gans, H.J. de, "Squat Effects o f Very Large Container Ships with D r i f t in a Harbor Environment", International Maritime-Port Technology and
Development Conference, September 2007, M T E C 2007, Singapore, ISBN:978-981 -05-9102-1
[12] ICORELS, "International Commission for the Reception o f Large Ships, ICORELS Expression i n Seehafenzufahrten - E i n Leitfaden zur Bemessung (Ubersetzung) P I A N C / I A P H A G n-30. Bulletin Nr. 95, Bonn 1997.
[13] Lap, A.J.W., "Fundamentals o f Ship Resistance and Propulsion Part A : Resistance", Publicati-on No.129a o f the N.S.M.B., Reprinted f r o m International Shipbuilding Progress (I.S.P.)Rotterdam
[14] Newman, J.N., "Marine Hydrodynamics", I S B N 0¬ 262-14026-8, The M I T Press, Cambridge,
Massachusetts and London, England, 1977
[15] Newman, J.N., "The Green Function f o r Potential Flow i n a Rectangular Channel", Journal o f Engineering Mathematics 26 pp.51-59, Kluwer Academic Publ., Printed in the Netherlands, 1992
[16] Schuster, S., "Untersuchingen über Strömungs- und Widerstand-verhaltnisse bei der Fahrt van Schiffen in beschranktem Wasser"
[17] Schmiechen, M.,"Squat-Formeln, Das S c h i f f i n begrenzten Gewassern",18 Duisburger K o l l o q u i u m Schiffstechnik / Meerestechnik, Duisburg, 1997 [18] Timman, R., Hermans, A . J . \ & Hsiao, G.C.,"Water Waves and Ship Hydrodynamics: A n Introduction", I S B N 90-247-3218-2, Martinus N i j h o f f Publishers and D e l f t University Press, Delft, the Netheriands, 1985 [19] Tuck, E.O. \ & Taylor P.J., "Shallow wave problems in ship hydrodynamics",8th On Navel Hydrodynamics, pages 627-659, Rome 1970
[20] Uliczka, K . , "Das Schiff in Wechselwirkung m f t der Wasserstrasse (The ship in interaction w i t h the waterway)", Verkehrswasserbau an
Seeschifffahrtsstrassen (Hydraulic engineering applied to approach channels, 13-15 June 2002
[21] Yeung, R.W., "Application o f a Slender-Body Theoiy to Ships M o v i n g i n Restricted Shallow Waters", Proceeding o f Symposium on Aspects o f Navigability, Delft, 1977
2nd International Conference on Ship Manoeuvring in Shallow and Confined Water: Ship to Ship Interaedon
8 A U T H O R S B I O G R A P H Y
Henk de Koning Gans holds the current position o f
assistant professor at D e l f l University o f Technology. He is responsible for the education and research o f mathematical and numerical ship hydromechanics. His previous experience includes shallow water problems, panel methods. He applied the panel methods for propeller calculations, free surface (wave pattern) calculation and o f passing o f ships.
