1174399573640-JIP Shielding Model Final

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Nationaal Lucht- en RuimtevaartlaboratoriumNationaal Lucht- en RuimtevaartlaboratoriumNationaal Lucht- en RuimtevaartlaboratoriumNationaal Lucht- en Ruimtevaartlaboratorium

National Aerospace Laboratory NLR

COMPANY CONFIDENTIALCOMPANY CONFIDENTIALCOMPANY CONFIDENTIALCOMPANY CONFIDENTIAL

NLR-CR-2003-018

Initial development of a method to account forInitial development of a method to account forInitial development of a method to account forInitial development of a method to account for

wind shielding effects on a shuttle tankerwind shielding effects on a shuttle tankerwind shielding effects on a shuttle tankerwind shielding effects on a shuttle tanker

during FPSO offloadingduring FPSO offloadingduring FPSO offloadingduring FPSO offloading

A.C. de Bruin

This study has been made as part of the “Overslag Optimalisatie” Joint IndustrialProject (JIP). For the work Bluewater/MARIN has contracted DNW (Marin project16656). The work is performed by NLR under subcontract with DNW (DNW purchase order 22.0555).

Customer: German-Dutch Wind Tunnels

Contract number: -

Owner: Bluewater

Division: Fluid DynamicsDistribution: Limited

Classification title: Unclassified

January 2003



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Summary

Wind and underwater forces on an offloading tanker that is approaching an FPSO (Floating

Production and Storage Offloading unit) are influenced by so-called shielding or shadow

effects, caused by the distorted wind and water flow fields in the wake of the FPSO.

An offloading tanker approaching an FPSO will experience changing flow conditions that

require adequate steering inputs for a safe continuous approach to the FPSO. For estimating the

wind-induced and underwater flow forces and moments on the offloading tanker at arbitrary

positions in the neighbourhood of the FPSO a predictive model is needed. After careful analysis

of available wind tunnel test data a method is proposed to compute the forces and moments on a

ship in the wake of an FPSO. The method requires that the disturbed velocity field behind theFPSO and the forces and moments on the shuttle tanker (unshielded conditions) are known. The

model is verified against the available wind tunnel data.



COMPANY CONFIDENTIAL

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Contents

List of symbols 5

1 Introduction 7

2 Discussion of experimental results from tests in DNW-LST wind tunnel 7

2.1 Introduction 7

2.2 Test set-up 7

2.3 The measured flow fields 8

2.4 Measured forces and moments 11

2.4.1 Forces and moments on the offloading shuttle tanker (without wind shielding) 13

2.4.2 The effect of the wind shielding on the shuttle tanker 17

3 An aerodynamic interaction model for wind shielding effects 18

4 Conclusions and recommendations 23

5 References 25

5 Tables

47 Figures

Appendix A Drag coefficient of the shuttle tanker when based on the frontal wind

exposed area 731 Table

2 Figures

Appendix B Application of slender wing theory for deriving an empirical formula for

the side force coefficient CL 761 Figure

Appendix C Computation of Cx and CM,z values with ESDU method 78

1 Table

(80 pages in total)




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List of Symbols

A Aspect ratio of the ships hull (analogy to a low-aspect ratio wing, see App. B)

Aref Reference area, see equation 2

b effective “wing span” of the ship hull (see App. B)

a, b, H cube dimensions (used in App. C)

c length of the ship

C force coefficient, defined in equation 2

CM moment coefficient, defined in equation 2

dM moment arm lengths, defined in equation 5

F force

L reference length for definition of moment coefficient, defined in equation 2

M moment

q dynamic wind pressure (q=½ρV2)

qref reference dynamic pressure (here taken as average dynamic wind pressure between

z=0 and z=52 m full scale, see also equation. 2)

18q average wind pressure between z=0 and z=18 m (full scale)

V velocity in wind-field

Vref reference velocity, see equation 2

V10 (undisturbed) wind velocity at 10 m above sea levelx, y, z flow axis system, defined in figure. 3

zref reference height used for the wind profile (equation 1)

Greek symbols

α power used in wind profile formula (see equation 1)

β orientation of the FPSO or shuttle tanker with respect to the undisturbed wind

∆β change in wind direction (with respect to undisturbed wind) in wake of the FPSO

18β∆ average change in wind direction between z=0 and z=18 m height and for a certain

segment of the shuttle tanker ρ air density

sub-fixes

bow for bow segment of the shuttle tanker

middle for middle segment of the shuttle tanker

stern for stern segment of the shuttle tanker

ref reference condition

x, y, x x-, y- or z component

D drag, see equation 3

L “lift”, see equation 3




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1 Introduction

As part of the Offloading Operability Joint Industry Project (JIP: see Ref. 1), Marin granted a

study to DNW concerning the wind shielding effects on a shuttle tanker that is approaching an

FPSO (Floating Production and Storage Offloading unit). The present study by NLR is part of

this project. The aim of the study is to define a methodology for the prediction of wind and

underwater forces on an offloading tanker that is approaching an FPSO. These forces are

influenced by so-called shielding or shadow effects, caused by the distorted wind and water

flow fields in the wake of the FPSO. Therefore an offloading tanker approaching an FPSO will

experience changing flow conditions that require adequate steering inputs for a safe continuous

approach to the FPSO. For estimating the wind-induced and underwater flow forces andmoments on the offloading tanker at arbitrary positions in the neighbourhood of the FPSO a

predictive model is needed. Previous work on this subject has been reported in references 2 and

3.

After careful analysis of available wind tunnel data from DNW a calculation method is

proposed that takes into account the changed flow conditions in the wake of the FPSO. The

method is verified against wind tunnel data.

2 Discussion of experimental results from tests in DNW-LST wind tunnel

2.1 Introduction

A brief description of the tests and the initial test results has been given in reference 3. Here a

more detailed discussion of the results is given.

2.2 Test set-up

Tests have been performed in the DNW-LST low-speed wind tunnel, which has a tunnel cross

section of 2.25x3 m2. All tests were done at a tunnel speed of roughly 30 m/s. An atmospheric

boundary layer, characteristic for sea conditions (so-called sea2 profile), was simulated. Two

1:400 scale model tankers were employed (see Figs. 1 and 2). Both tankers have a similar shape,

but the FPSO has an extra deck load. The offloading shuttle tanker was divided in three model

segments (bow, middle and stern segment) of equal length (100 m full scale). These three

segments were always tested together, but model forces could be separately measured for each

model segment (but with the other segments still in place).




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The tests consisted of three parts.

During rest run 4 until 21 (see Tab. 1) flow field traverses were made with a 5-hole rake, while

only the FPSO tanker was placed in the wind tunnel. The rake has 18 probes with a probe pitch

of 15 mm., but during the present tests only 17 probes were used. It was placed at fixed

x-position in the tunnel and was traversed in y-direction. The FPSO model was placed at nine

different positions with respect to the rake. Positions of the wake traversing planes and the

model are sketched in figure 3. The tunnel centre-line is at y=0 and the model centre is at x=0.

Only two model yawing angles (β= 195 and β= 210 degrees) were tested, yielding in total 18

flow fields. For each case an y-traverse was made with the lowest tube of the 5-hole rake at

17.5 mm (7 m full-scale) above the tunnel floor and an extra traverse a half probe pitch further from the tunnel floor (so at 25 mm, or 10 m full scale). All three velocity components were

measured with the rake.

In a second series of measurements (runs 22-25) the forces on the shuttle tanker were measured

in the absence of the FPSO. A six-component external force balance was placed below the

rotation table centre. Either forces on the total model or on the bow-, middle- or stern-segment

of the shuttle tanker were measured. First the forces were measured during a continuous β-

sweep (see polar 1 runs in Tab. 1; yawing angle β between –180 and +180 degrees). Then the

forces were also measured during a step-by-step (limited) β-sweep (see polar 2 runs in Tab. 1).

These tests represent the unshielded test conditions.

In a third series of measurements (runs-26-33) additional test runs with the FPSO at three

positions relative to the shuttle tanker were made (see Figs. 3 and 4). Forces were measured on

either the bow-, middle- or stern-segment as well as on the complete model. Forces were

measured in a limited β-range. Again both continuous and step-by-step measurements were

taken. The data were processed into self-descriptive NLR Tout-file format.

2.3 The measured flow fields

Flow field measurements around and behind the FPSO were taken at nine downstream positions

in the wake (x= -0.50 (0.25) 1.50 m) and for two oblique model orientations (β=195 and β= 210

degrees, see Fig. 3 for a sketch of the wake measurement plane positions with respect to the

FPSO model). Flow velocity components (Vx, Vy, Vz) have been measured in a tunnel-fixed co-

ordinate system. Measured flow fields are shown in figures 5 (β=195) and 6 (β=210). The

vectors show the cross-flow velocities and the magnitude of the axial velocity is indicated by

the colour. Close to the FPSO the flow could not be measured with the rake. Nevertheless it is

clear that at the leeward side of the FPSO a strong re-circulation region with substantial reduced

Vx occurs. The flow over the ship creates a strong vortex along the leeward side of the ship.

Immediately downstream of the stern of the model (at x=0.50 m), the centre of the vortex has

substantially moved to the left. Both the centres of the vortex and the wake are found in the lee




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ships hull (ymin, ymax) are given in table 2. For x/c > 1 or x/c< 0, a straight extension of the ships

“hull ” was assumed. When referring the lateral positions given in table 2 to the flow field data

shown in figures 5 and 6, it is obvious that the bow of the shuttle tanker is well within the

disturbed flow field. However the stern of the shuttle tanker moves well out of the disturbed

flow field, especially with more downstream model positions and for the β=210 case.

For the derivation of average flow conditions the dynamic pressure and the flow angle data for

each z-position were first spatially averaged between ymin and ymax (see Tab. 2), yielding q(z)

and ∆β(z) profiles. In a second step these values where further spatially averaged (arithmetic

mean value of measured data points) between z=0.0175m (the first data point: at 7m height full

scale) and height z, yielding )z(q and )z(β∆ profiles. It should be noted that this is only anapproximation of the average value between the tunnel wall and height z. Averaged profile

results (∆β(z), )z(β∆ , q(z)/qref and ref q/)z(q ) are shown in figures 8 (for β=195) and 9 (for

β=210).

Average values at z=18 (the height of the hull) and at z=45 m (the height of the steering house)

are of specific significance. Values for ref 18 q/q , ref 45 q/q , 18β∆ and 45β∆ are given in table

3. It should be noted that ref q refers to the atmospheric boundary layer profile of the undisturbed

flow. At the x=0.5 m measurement plane very large changes in flow angle are found, especially

at low z-values. For the same station also very low dynamic pressures are found at some

distance from the ground. It is clear that the flow conditions vary considerably along the centre

line of the shuttle tanker.

This becomes more clear when plotting ref 18 q/q , ref 45 q/q , 18β∆ and 45β∆ as function of the

non-dimensional wake intercept position x/c (x/c=0 corresponds with the bow of the shuttle

tanker and x/c=1 corresponds with the stern, c is the length of the ship). Figure 10 shows the

results for the β= 195 case, for each of the three ship positions investigated. Large flow angles

changes only occur near the bow of the ship when it is at position 1 (x=0.125 m). Considerable

deviations in dynamic pressure are observed, especially near the bow of the ship. For the β= 210

degrees case (see Fig. 11) the flow conditions vary much more pronounced along the length of

the ship than for the β=195 case.

Average flow conditions for each of the model segments were derived as well. Results are given

in table 4. Consequences of the changed flow conditions for the forces and moments on the

shuttle tanker will be discussed in section 3.




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Instead of considering Cx and Cy (body fixed force components) it is also useful to consider CD

and CL (flow-oriented force components, defined in a rotated flow-axis system as shown in Fig.

13). The following relations apply:

β+β−=

β+β=

cosCsinCC

sinCcosCC

yxL

yxD(Eq. 3)

With given force and moment coefficients it is in principle possible to compute the application

point for the total force. Its location with respect to the balance centre follows from the

following relations (three equations and three unknowns):

0)xCyCLC(AqxFyFM)y,x(M

0)zCxCLC(AqzFxFM)z,x(M

0)yCzCLC(AqyFzFM)z,y(M

yxz,Mref ref yxz

xzy,Mref ref xzy

zyx,Mref ref zyx

=∆+∆−=∆+∆−=

=∆+∆−=∆+∆−=

=∆+∆−=∆+∆−=

(Eq. 4)

Unfortunately, the above set of equations has no unique solution for ∆x, ∆y, ∆z because the

determinant of the set of equations is zero. One can define “force application distances” (sign of

the moment coefficients has been kept for convenience):

2

y

2

xz,Mz,M

2

z

2

xy,My,M

2

z

2

yx,Mx,M

CC/LCd

CC/LCd

CC/LCd

+=

+=

+=

(Eq. 5)

Adequate summing of the forces and moments measured for the separate segments yields the

forces and moments on the complete model:

)FF(*100MMMM

)FF(*100MMMM

MMMM

FFFF

stern,y bow,ystern,zmiddle,z bow,zz

stern,z bow,zstern,ymiddle,y bow,yy

stern,xmiddle,x bow,xx

stern,middle, bow,

−+++=

−+++=

++=

++= ξξξξ

(Eq. 6)

Where the distance between the bow and stern force balance centres and the model centre is

equal to 100m (full scale), see also figure 14. If all measurements are perfect, the sum of the

forces measured for the different model segments should be equal to the force measured on the

complete model. This provides a useful consistency check.




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2.4.1 Forces and moments on the offloading shuttle tanker (without wind shielding)

Before discussing the force measurements it is useful to consider the qualitative behaviour of

the forces and moments on the offloading shuttle tanker in relation to the yawing angle of the

ship and the flow around the ship. This is sketched in figure 15.

Wind-facing sides of the ship are exposed to a high stagnation pressure, whereas lower

pressures are found at the leeward side of the ship. Asymmetric flow conditions induce high

flow velocities and low pressures in the neighbourhood of corners and thus create a side force

component CL normal to the oncoming flow. Such low pressure areas are particularly strong

near the windward facing corners and therefore side forces tend to apply on the windward

facing sides and create a yawing moment as sketched in figure 15. The steering house is mainlya drag inducing body (though there may also be a small side force acting on it) and this will give

a significant contribution to the total yawing moment, because of the relatively large momentum

arm. It is interesting to note that in the β-range between 90 and 180 degrees, the contribution of

the steering house to the yawing moment is expected to be of opposite sign than that of the

ship’s hull.

In the force and moment coefficients data plots, lines will represent the data taken during

continuous β sweeps and symbols represent the corresponding data points from step-by-step

measurements. In all cases a good agreement between both data sets is found.

The measured force coefficients are shown in figure 16. The axial force coefficient Cx is zero

when there is pure cross-flow (β= 90 or 270 degrees) and becomes largest for β= 180 (flow to

the bow of the ship) and for β≈ +/- 30 degrees (somewhat oblique flow from the stern).

Similarly, the side-force Cy is zero for β= 0 and 180 degrees and becomes larger during cross-

flow conditions (β= 90 and 270 degrees). Largest Cy values are observed for β≈ 115 and 245

degrees. The flow over the ship causes relatively low pressures above the ship and consequently

a substantial positive value for Cz, especially under pure cross-flow conditions. But compared to

the weight of the ship this force is still negligible. Peculiarly enough Cz is not symmetric with

respect to β= 180 degrees, even though the ships geometry is almost perfectly symmetric. This

points to a potential problem with the measurement of vertical forces (and the corresponding

momentum coefficient CM,y). Probably the airflow through the slit between the model and the

tunnel floor of the wind tunnel is rather sensitive to the exact geometry of the slit. This will

cause distributed pressures below the model, which potentially have an influence on Cz, CM,y

and CM,z. Fortunately, no effect on the more important Cy , Cx and CM,z coefficients is to be

expected from this.




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Flow oriented force coefficients CL and CD have been derived from equation 3 and are shown in

figure 17. The drag is smallest for β =0 degrees (flow from the back), and becomes larger in

cross-flow conditions. In itself it is rather surprising that the drag is smallest with flow from the

stern, however the drag is composed of two terms: drag due to the pressure field around the

model and drag due to friction forces. With flow from the stern, one should expect a

considerable wake and corresponding pressure drag term for the steering house. But the wake of

the steering house implies relatively low (or even reversed) velocities over the ship’s deck. So

low friction forces are to be expected on this part of the ship. Apparently, this results in a

comparatively low total drag of the ship during flow from the stern conditions.

It should be noted that the drag coefficient is based on a constant reference area, whereas in thecase of a ship’s hull, the frontal projected area A proj of the ship does strongly depend on the

direction of the flow. It is therefore no surprise that quite substantial changes in drag coefficient

(about 40 % around the mean value) are found, depending on flow direction. It was tried

whether with a method taking account of the actual projected frontal area’s and the effective

dynamic wind pressures of the different model segments (hull, steering house and upper

steering house part) a more constant drag coefficient is found. The method is described in

Appendix A and the result, shown in figure A-2, shows indeed less (20%) variation in*

DC values.

As a consequence of model symmetry conditions CL is zero for β= 0 and β= 180 degrees (see

Fig. 17). It also becomes equal to zero during pure cross-flow conditions (β= 90 and 270

degrees). Maximum CL is observed for β≈ 130 and 230 degrees. CL is always smaller than CD.

Closer inspection of the CL polar indicates a very slow change of CL with flow angle near β= 0

and a somewhat faster change near β= 180 degrees. This is followed by a more rapid change

further away from these points and a sudden drop in CL at still larger flow angles. This type of

behaviour resembles that of slender wings (wings with a long chord and a small span), which

display a slow linear lift increment followed by a rapid non-linear lift increment at larger angles

of attack. It is therefore tempting to apply slender wing theory to the present ship hull geometry.

As shown in Appendix B, with some proper empirical tuning this approach can give a

reasonable accurate model for CL.

Figure 18a shows that the angle between the force vector (Fx, Fy) and the flow vector reaches

values up to about 23 degrees. Figure 18b shows the CL-CD polar for the wind vector segments

90<β<180 (flow to the bow) and –90<β<90 (flow to the stern).

The moment coefficients are shown in figure 19. In the present study CM,z is of primeimportance. Its behaviour is anti-symmetric with respect to β. The peculiar behaviour near




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β=180 (flow from the bow) should be noted. It is probably due to the combined but opposite

effects of suction at the bow lee-side and drag forces on the steering house (see for explanation

Fig. 15). Apparently for flow angles between 160 and 200 degrees, the contribution of the

steering house to the yawing moment exceeds that of the hull.

The behaviour of the moment coefficient CM,x can be understood as the combined effect of the

wind pressure forces on the wind facing side of the ships hull and the existence of low pressures

over the wind facing side of the deck. Finally, it should be noted that the CM,y values are not

perfectly symmetric with respect to β=180 degrees. This is probably related to a measurement

problem (pressures below the model depend critically on the model suspension above the tunnel

floor) that was already noted when discussing Cz.

Force application distances have been computed with equation 5. The results are shown in

figure 20. The magnitudes are in qualitative agreement with the sizes of the ship. Small values

are found for dM,x (roughly up to about 20m, compared to 30 m half-width of the ships hull).

Large values are found for dM,y and somewhat smaller values for dM,z (up to about 60 m,

compared to 150 m half-length of the ships hull).

Force measurements have also been made for the stern, middle and bow segment separately.

Measurement consistency checks were made to check whether the sum of the forces and

moments on the different model segments (measured in three different runs) agree with the

forces and moments measured for the complete model. The checks have only been made for the

step-by-step measurement data points. Results for the model forces are shown in figure 21 and

for the moments in figure 22. A reasonable agreement is observed, except for Cz and for CM,y.

This is again most probably due to changing pressures below the model, that seem critically

depending to the model positioning close to the tunnel floor. More attention should be paid to

this in future measurements.

It is illustrative to consider the contributions of the different model segments to the total forces

and moments. The contributions to Cx, Cy and Cz are shown in figures 23-25. For Cx, by far the

largest contribution comes from the stern-segment of the model (due to the wind forces on the

steering house). The bow-segment contribution to Cx is much smaller. As to be expected with

the sign convention for Cx (see Fig. 13) the contributions from the stern and the bow segment

are positive with flow from the stern and negative with flow from the bow-side. Peculiarly

enough the contribution of the middle segment has an opposite sign. On the fully prismatic

middle section contributions to Cx should be expected from the friction forces. In principle,

negative friction forces might have been caused by (strong) back-flow over the upper deck, but




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this is unlikely to happen under oblique flow conditions (e.g. β= 30 degrees, where Cx attains its

largest negative value).

However, it is also possible that this, rather unexpected, behaviour is due to an unwanted

pressure difference over the front and back ends of the model segment. The middle segment has

been isolated from the bow and stern segment by simply cutting a tape covering a small slit

between the model segments. The slits between the model segments are in open connection with

the local pressure field surrounding the model and some average pressure may build up in the

slit. This can influence the axial forces measured for the individual model segments (but will

have no effect on the total sum of the Cx contributions).

For Cy the different model segments contribute as to be expected. The largest contribution is due

to the stern-segment (because of the presence of the steering house). Each segment attains a

maximum at a different flow angle: the stern-segment for β≈ 70 degrees, the middle-segment

for about β= 90 degrees and the bow-segment for about 120 degrees.

For Cz the contributions are predominantly positive (so a ship in wind conditions will be slightly

lifted). Maximum values are attained for roughly the same flow angles as observed for Cy. The

stern-segment gives weakly negative contributions near β= 0 and the bow-segment near β= 180

degrees. Measurements are not perfectly symmetric with respect to β= 180 degrees.

Figures 26 and 27 show the contributions of the model segments to the flow oriented force

coefficients CD and CL. The middle- and bow-segment of the model behave more or less similar,

whereas the stern-segment behaves more complicated with β. The stern-segment has the largest

contribution to the drag (because of the steering house). Near β=180 the gradients dCL/dβ for

the bow and middle-segment are about equal, whereas the gradient for the stern-segment is of

opposite sign. Near β=0 degrees the stern- and middle-segments have quite similar behaviour in

CL values, whereas the CL values for the bow-segment remain much smaller.

Figure 28 shows that the model segments have about equally sized contributions to the model

coefficient CM,x, albeit max contributions occur at different flow angles. Figures 29 and 30 show

the contributions of the different model segments to the moment coefficients CM,y and CM,z. For

the bow- and stern segments the contributions of the Cy and Cz terms (see equation 6) have been

included. The Cy and Cz contributions to CM,y and CM,z appear the most important ones. For this

reason CM,z of stern- and bow-segments closely resemble Cy (Fig. 24). Similarly, CM,y

contributions of stern and bow closely resemble Cz (Fig. 25). The middle-segment of the model

has only a very small contribution to CM,y and CM,z.




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2.4.2 The effect of the wind shielding on the shuttle tanker

Forces and moments on the entire shuttle tanker have only been tested in a β-range between 90

and 270 degrees, for three different relative positions (see Figs. 3 and 4) with respect to the

FPSO. Just as for the unshielded case, the forces and moments on the different model segments

have also been measured, albeit in a sometimes further reduced β-range. We start the discussion

with the forces and moments on the total ship configuration.

The force coefficients for the three model positions are compared with the unshielded results in

figure 31. The shielding effects on the force coefficients seem at first sight rather modest. When

part of the shuttle tanker is in the wake (for the present test set-up this is primarily the case for

flow angles near or slightly beyond β= 180), the reduced velocities in the wake lead to a lower absolute value of Cx. There is a sharp maximum effect on Cx at about β=200 degrees. The effect

is largest for the most upstream model position, but the effect reduces only slowly with the

distance between both models. It is interesting to note that, especially for the x=0.125 m case,

there is also a measurable effect on Cx for the pure cross-flow condition β=90. This is clearly no

wake-effect, but is probably due to flow blockage by the hull of the FPSO. This deflects the

flow such that it hits the bow of the shuttle tanker, thereby causing a force in negative x-

direction.

The wind shielding effect on Cy is mainly visible between β= 180 and 260 degrees. It seems to

be caused both by a pure wake effect (leading to lower dynamic wind pressures and thus lower

forces) and by the deflected flow angle in the wake region (see the flow field data in figures 5

and 6). The deflected flow field causes a lower effective model side-slip angle, it is as if the

results for Cy are shifted in β. Some other effects on Cy are visible near β= 90 degrees.

The shielding effects on the drag and lift coefficient are shown in figure 32. The physical

explanation for the differences follows from the discussion of Cx and Cy values.

The shielding effect on the moment coefficients is shown in figure 33. The shielding effect on

CM,x is quite similar to that on Cy and is thus probably related to the changes in the (distributed)

side forces, because of the changed flow direction in the wake of the FPSO. Some shielding

effects are also visible near β= 90 degrees.

Increased CM,y values are found between β=180 and 270 degrees. According to the flow field

measurements (see Figs. 5 and 6) in this β-range a considerable down wash will occur near the

bow of the FPSO, but rapidly less down wash further downstream. This will create negative

distributed Cz forces in the bow area, causing a positive contribution to CM,y. Some shielding

effects are also visible for β below 180 degrees.




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Similarly, in this β-range, FPSO induced side slip angles will cause positive distributed side

forces, especially near the bow, and to a smaller extend to the stern of the shuttle tanker

(because of decreasing induced side-slip angle at larger distances behind the FPSO), thus

leading to a positive contribution to CM,z (see Fig. 13 for the sign conventions). Some shielding

effects are also visible for β below 180 degrees.

Further insight in the shielding effects can be obtained by inspecting the contributions of the

different model segments during wind shielding conditions. Results, shown in figures 34-39,

indicate that (at least for the relative model positions tested here) the bow-segment of the model

has by far the largest wind-shielding contribution to the force coefficients Cy and Cz and to the

moment coefficients CM,y and CM,z. It is further interesting to note that at the upstream positionx=0.125 m, the Cz (and consequently also CM,y) contribution of the bow-segment displays a

sudden change near β=225 degrees, probably due to a sudden change in flow pattern over the

bow-segment of the model.

It should be noted that the measurement results for CM,x (see Fig. 37) are not well understood

and also not consistent with the measurements for the complete ship. Summing of the different

model part contributions suggests a considerable total wind shielding effect on CM,x for the

complete β-range, whereas measurements on the whole ship model (see Fig. 33a) yield only

shielding effects in a limited β range.

3 An aerodynamic interaction model for wind shielding effects

A method to compute aerodynamic forces on a geometry consisting of prismatic elements is

presented in Appendix C. The method is based on the ESDU data-sheet methodology. In

Appendix C it is applied to the unshielded shuttle tanker case, for flow angle conditions β= 0

and 90 degrees. Unfortunately the predicted force coefficients appear larger than the measured

ones. Nevertheless, elements of the general methodology presented in Appendix C are still

useful for the development of a wind shielding calculation procedure. Instead of computing the

total force the wind shielding calculation procedure will be based on measured forces and

moments for the undisturbed (unshielded) flow situation.

For calculation of the ship movements the forces Fx, Fy and the moment Mz are of prime

importance. In an unshielded situation these will depend on the wind direction, the shape of the

wind profile and the wind strength (defined as the wind velocity at a certain height).




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For the unshielded situation, measurements on a model placed in a wind tunnel can give

accurate results for the force and moment coefficients for all wind directions . Proper re-scaling

with the actual scale of the ship and the actual wind velocity will yield Fx, Fy and Mz under all

wind conditions.

As shown in section 2.3, for the shielded case, the local flow velocity and its direction can be

considerably different from the unshielded situation and this will have an impact on Fx, Fy and

Mz of the shuttle tanker. If flow field properties downstream of the FPSO tanker (and in the

absence of the shuttle tanker) are known, these might be a starting point for calculating the

forces and moments on the shuttle tanker. However, this implicitly assumes that the effective

wake flow field immediately upstream of the shuttle tanker is the same as for the case withoutshuttle tanker. In other words: a “frozen” wind field is assumed behind the FPSO tanker. It is

clear that this assumption neglects possible interference effects that the shuttle tanker can have

on the development of the wake flow behind the FPSO. E.g. the presence of the shuttle tanker

should not significantly alter the forces and the flow topology around the FPSO (e.g. the

location of flow re-attachment behind the FPSO). This becomes less true if both ships come

closer to each other, as is tentatively sketched in figure 40. No precise definition can be given

on what has to be considered as too close. For very close ship positions perhaps the only

solution for accounting for the shielding effects is to use an experimental data-base for all

relative model distances and orientations. For the time being a “frozen” velocity field is

assumed for calculating the forces and moments on the shuttle tanker under shielded conditions.

Comparison of calculated and measured values will bring further insight into the validity

boundaries of this assumption.

The following calculation procedure was tested:

1. Averaged frozen wind field properties along the centre-line of the shuttle tanker were

determined. These results were further averaged for the different model segments, yielding

average flow conditions within the internal volume of each shuttle tanker segment

( 1818 ,q β∆ for the bow- and middle-segment and 4545 ,q β∆ for the stern-segment, see Tab.

4 and section 2.3).

2. Forces and moment data (Fx(β), Fy(β), Mz(β)) of all β-sweeps were averaged in order to

suppress the scatter in the experimental data (due to measurement in turbulent flow

conditions. A five point spatial averaging method was used.

3. From the smoothed unshielded force data (e.g Cx(β)) of each model segment, the force and

moment coefficients at the effective mean flow angle were taken ( 18β∆ for the bow and

middle-segment and 45β∆ for the stern part). These are intermediate results only and are

shown in figures 41-46 as the green data points (legend: calculated (beta)).




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4. These force and moment coefficients were re-scaled with the effective mean dynamic

pressure ratio ( unshielded,1818 q/q for the bow- and middle-segment and unshielded,4545 q/q for

the stern-segment). These results are shown in figures 41-46 as the blue data points (legend:

calculated (beta, q)).

5. Contributions to the total moment coefficient ∆CM,z were determined with equation 6.

6. Computed forces and moment contributions of the different model segments were summed.

Wind-shielding calculation results for Cx, Cy and CM,z and for β= 195 and 210 degrees are

shown in figures 41-46. The data are first shown per model segment. Blue data-points are the

final calculated data, whereas the red data-points are the measured data (measured by

segments). The green data-points are intermediate results (only corrected for ∆ β ), and the black

data-point was measured in the unshielded situation for the nominal flow angle. The calculation

procedure seems satisfactory in most cases (e.g. Cy and ∆CM,z for bow-segment), but is less

convincing in some other cases.

For the total forces and moments two different measured data sets are shown. Both are based on

the smoothed data of the β-polar, but one is based on the measured force on the total model

(filled black and red symbols) and one is based on the summed contributions from the different

model segments (open black and red symbols). As discussed in section 2.4 the summed data for

the different model segments do not always agree with the measured data on the complete

configuration. The calculation (open blue symbols) is based upon summation for the different

model segments and should therefore be compared with the open red symbols.

The data in figures 41-46 are presented on arbitrary scales. To get a better impression of the

significance of the deviations found, the total calculation results have been plotted together with

all relevant data (including β-sweeps) in figure 47. The lines represent smoothed β-sweep data

(both for the unshielded as well as for the shielded cases). Dots are shown at the tested

geometrical yawing angle of the model. The black closed dots represent summed measured data

of the different model segments for the unshielded situation. The open dots represent summed

measured data for the shielded case. The filled dots represent the computed data (and should be

compared with the corresponding open symbols). The proposed calculation method produces

results in reasonable agreement with the measurements. It is however clear, that the differences

between summed and total measured data imply quite some uncertainty in the experimental data

and thus also in the correctness of the calculation procedure which is based on a calculation by

segments.




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Remarks on a possible alternative calculation procedure

Alternative calculation procedures for the forces and moments in the wind-shielded situation are

possible and should be mentioned for possible further evaluation.

First of all it has to be noted that the proposed calculation method is based on segmentation of

the model in three segments. This is because force measurement data were available for the

bow-, middle- and the stern segment of the shuttle tanker. However, this segmentation is quite

arbitrarily. It might e.g. be better to distinguish the steering house as a separate entity. This

extends far above the ship hull and has a different aerodynamic behaviour. It also has an

important influence on the yawing moment. Separate weighing of this model segment would

probably lead to improved understanding of the forces and moments in relation to the flowangle β. Also the aerodynamic forces on this cubic shaped part seem more amenable to

modelling than those of the entire (complex shaped) stern-segment.

In the tested calculation method “volume averaged” flow conditions q and β∆ of the different

segments were used to calculate the force and moment coefficient for each segment. The total

force and moment follows from summation over the segments. The following general relations

apply for deriving the volume averaged flow conditions (Ni flow field data-points in model

segment i):

) j( N

1

) j(q N

1q

i

i

N

1 ji

i

N

1 ji

i

∑

∑

=

=

β∆=β∆

=

(Eq. 7)

And the force and moment coefficients for model segment i then follow from:

)(Cx)(C

)(Cq/q)(C

)(Cq/q)(C)(Cq/q)(C

shielded,i,yishielded,i,z,M

iunshielded,i,z,Munshielded,ishielded,ishielded,i,z,M

iunshielded,i,yunshielded,ishielded,ishielded,i,y

iunshielded,i,xunshielded,ishielded,ishielded,i,x

β×∆=β∆

β∆+β=β

β∆+β=ββ∆+β=β

(Eq. 8)

The force and moment of the total configuration (Ns segments) then follow from:




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[ ]∑

∑

∑

=

=

=

β∆+β=β

β=β

β=β

s

s

s

N

1i

shielded,i,z,Mshielded,i,z,Mshielded,z,M

N

1i

shielded,i,yshielded,y

N

1i

shielded,i,xshielded,x

)(C)(C)(C

)(C)(C

)(C)(C

(Eq. 9)

The usage of bulk averaged properties q and β∆ is not necessarily the best choice to make.

E.g. if locally large flow angles occur, these can have a relatively large impact on the moment

Mz, but by using a volume averaged β∆ value this local information is lost. Also Cx(β), Cy(β)

and CM,z(β) are generally non-linear functions of β and it is therefore not obvious that a volume

averaged β∆ will lead to the optimum result.

Instead of using bulk volume averaged properties q and β∆ one could also use a “distributed

forces” model, which more naturally takes account of distributed flow variations. In this

procedure the volume averaging step for obtaining q and β∆ is replaced by a direct volume

averaging of the force and moment coefficients. If the internal volume of each tanker segment i

consists of Ni equally sized volume elements and the local flow conditions q and ∆β are given,

the following volume integration procedure applies:

∑

∑

∑

∑

=

=

=

=

β∆+β×∆×=β∆

β∆+β×=β

β∆+β×=β

β∆+β×=β

i

i

i

i

N

1 j junshielded,i,y jshielded,i

iunshielded,ishielded,i,z,M

N

1 j

junshielded,i,z,Mshielded,i

iunshielded,i

shielded,i,z,M

N

1 j

junshielded,i,yshielded,i

iunshielded,i

shielded,i,y

N

1 j

junshielded,i,xshielded,i

iunshielded,i

shielded,i,x

)(Cx) j(q Nq

1

)(C

)(C) j(q Nq

1)(C

)(C) j(q Nq

1)(C

)(C) j(q Nq

1)(C

(Eq. 10)

The total force and moment coefficients for the Ns segments follow again from equation 9.

It is also possible to first perform average q and ∆β along the height of the segment and then

replace equation 10 with an integration over the ground surface of the segment. For linear

relationships between the force and moment coefficients and β the above sketched distributed

surface alternative calculation procedure will lead to equal results for the force coefficients, but

the computed value for ∆CM,z is not necessarily the same, because it takes account of the actual

momentum arms ∆x j.




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4 Conclusions and recommendations

Flow measurements

The measurements with the 5-hole rake yield good flow field data, but are relatively sparse in x-

direction (∆x is 1/3 of the length of the shuttle tanker). In case that a more refined validation of

the proposed wind-shielding calculation method is to be made, it is recommended to measure

additional intermediate flow field planes in order to reduce the flow errors in the flow averaging

step of the calculation method.

Development of a flow field modelThe proposed calculation method for the shielding effect requires detailed knowledge of the

wake flow field for all FPSO model wind headings. Such wake measurements are only

affordable for a limited number of flow conditions, e.g. for validation of the wind-shielding

calculation method. In practice it is not possible to perform that many elaborate measurements.

In principle two options remain:

• Measurement of the initial flow field (for different flow angles) and calculation of the flow

further downstream. Initial attempts by Marin to calculate the wake flow where not yet

successfully.

• Development of an analytical wake model based on measured forces on the FPSO. It is

known that the velocity defects in the wake are related to the drag and that the cross-flow

∆β is related to the side force on the FPSO model. It is proposed to relate the wake

properties directly behind the FPSO to these measured forces and develop empirical

relations for the downstream development of the wake. Existing flow field data for β=195

and 210 degrees can be used to test such a flow field model.

Force measurements

During the analysis of the force measurement data, inconsistencies were found between

measurements for the whole shuttle tanker model and the summed contributions of the three

model segments. These problems are summarised below.

• Detailed inspection of the force and moment data reveal that the large (5 mm) slit between

the model and the tunnel floor is probably causing a problem with the measured forces. The

flow through this slit will create a pressure distribution below the model that is probably

quite sensitive to the exact geometry of the slit. It will mainly influence Fz but can also have

an influence on the moment coefficients CM,y and CM,x. Discrepancies in these coefficients

are observed when comparing the summed forces and moments of the different model

segments with the forces and moments measured for the entire model. More attention

should be paid to this phenomenon in future wind tunnel tests, e.g. by using some sort of




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labyrinth sealing between the bottom of the ship and the tunnel floor or by using a more

narrow slit (e.g. 1 instead of 5 mm).

• Similarly, the measurement by segments allows a pressure build-up in the slit between the

model parts. A static pressure field is to be expected. However, this may quite critically

depend on the details of the gap geometry (especially at the wind facing parts, where any

misalignment between the two model-parts can have a large effect). This can have an effect

on Cx and to some extend also on CM,y and CM,z. Indeed the measurements reveal some

mismatch between measured Cx on the total configuration and the summed contributions of

the model segments. There are some peculiarities on measured Cx for the middle segment

(the force is directed against the prevailing wind direction). In future experiments it should

be attempted to diminish these problems by applying a suitable labyrinth sealing betweenthe model segments.

In addition it was noted that the segmentation of the model in a bow-, middle- and stern

segment is quite arbitrary. Other segmentations are feasible. In particular it was remarked that

the aerodynamic properties of the steering house will be quite different from that of the ship

hull. Putting these together in one model segment (the stern) is not very logical. It would

probably have been better if the steering house would be considered as a separate segment,

either by measuring it separately, or by calculating it separately (e.g. with an ESDU like

approach as sketched in App. C).

Calculation method for wind shielding effects

A method for calculation of the forces and moments for situations with wind shielding was

presented and tested. The method in its current version utilises volume averaged flow quantities

q and β∆ for the different model segments (bow-, middle- and stern) and the measured force

and moment coefficients for the unshielded case. Encouraging results were obtained, but some

further testing of the method (for other relative model positions and with more accurate force

measurements on the different model segments) is recommended. A potentially better

calculation procedure (the so-called “distributed forces” method) has been proposed, but still

needs to be tested

Stability of the flow field

A necessary requirement for modelling the movement of the shuttle tanker in the wake of the

FPSO is that that the flow-field is sufficiently steady such that the periodic changes in the flow

do not lead to significant unsteady movement of the tanker. So far no data have been gathered

on the unsteadiness of the wake flow. It is recommended to explore the frequency content of the

wake flow with a single hot-wire or hot-film probe as part of a future test campaign.




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5 References

1. Anon.: Project plan Overslag Optimalisatie (in Dutch), version 2.0, 27-03-2002.

2. Fucatu, C.H.; Nishimoto, K.; Maeda, H.; Masetti, I.Q.; The shadow effect on the dynamics of

a shuttle tanker , Proc. 20th International Conference on Offshore Mechanics and Arctic

Engineering, OMAE, 2001.

3. Buchner, B.; Bunnik, T.; Wind shielding investigations for FPSO tandem Offloading ,

Presented at JSC, 2002.

4. Anon.: Prediction of wind and current loads on VLCCs, OCIMF 1994.

5. Anon.: Fluid forces, pressures and moments on rectangular blocks, ESDU Item Number

71016, September 1971.6. Anon.: Mean fluid forces and moments on rectangular prisms: surface-mounted structures in

turbulent shear flow, ESDU Item Number 80003, December 1979.

7. Hoerner, S.F.; Borst, H.V.; Fluid-Dynamic Lift , Hoerner Fluid dynamics, 2nd

edition, 1985.

8. Hoerner, S.F.; Fluid-Dynamic Drag , published by the author, 1958.




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Table 1 Overview of test conditions of initial DNW-LST FPSO/shuttle tanker shielding tests

series Run Polar ββββ Model balance RAKE / FPSO model Activity/

[#] [#] [#] [°] Configuration pos x [m] y [m] z [m] Remarks

3102 4 1 195 FPSO model - 0.500 -0.48 → 0.50 0.1375 rake traverse

2 195 FPSO model - 0.500 -0.48 → 0.50 0.1450 rake traverse






2 195 FPSO model - 1.250 -0.48→

0.50 0.1450 rake traverse



3102 9 1 195 FPSO model - 0.250 -0.48 → -0.17 0.1375 rake traverse

2 195 FPSO model - 0.250 0.05 → 0.50 0.1375 rake traverse

3 195 FPSO model - 0.250 -0.48 → -0.17 0.1450 rake traverse






3102 11 1 195 FPSO model - -0.250 -0.48 → -0.05 0.1375 rake traverse

2 195 FPSO model - -0.250 0.18 → 0.50 0.1375 rake traverse

3 195 FPSO model - -0.250 -0.48 → -0.05 0.1450 rake traverse


3102 12 1 195 FPSO model - -0.500 -0.48 → 0.06 0.1375 rake traverse


3 195 FPSO model - -0.500 -0.48 → 0.06 0.1450 rake traverse



2 210 FPSO model - -0.500 -0.48 → 0.50 0.1450 rake traverse



3 210 FPSO model - -0.250 -0.48 → 0.12 0.1450 rake traverse4 210 FPSO model - -0.250 0.40 → 0.50 0.1450 rake traverse










2 210 FPSO model - 0.500 -0.48 → 0.50 0.1450 rake traverse3102 18 1 210 FPSO model - 0.750 -0.48 → 0.50 0.1375 rake traverse




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series Run Polar ββββ Model balance RAKE / FPSO model Activity/

[#] [#] [#] [°] Configuration pos x [m] y [m] z [m] Remarks

2 210 FPSO model - 0.750 -0.48 → 0.50 0.1450 rake traverse3102 19 1 210 FPSO model - 1.000 -0.48 → 0.50 0.1375 rake traverse






3211 22 1 360→0 tanker bow - - - continuous

2 360→165 tanker bow - - - step-by-step

3231 23 1 360→0 tanker stern - - - continuous

2 360→165 tanker stern - - - step-by-step

3221 24 1 360→0 tanker middle - - - continuous2 360→165 tanker middle - - - step-by-step

3241 25 1 360→0 tanker total - - - continuous

2 360→165 tanker total - - - step-by-step

3341 26 1 270 → 90 FPSO + tanker total 0.125 0.125 - continuous

2 217.5→180 FPSO + tanker total 0.125 0.125 - step-by-step





3321 29 1 270 → 90 FPSO + tanker middle 0.375 0.125 - continuous

2 217.5→180 FPSO + tanker middle 0.375 0.125 - step-by-step

3321 30 1 270 → 90 FPSO + tanker middle 0.250 0.125 - continuous


3 270 → 90 FPSO + tanker middle 0.125 0.125 - continuous


3311 31 1 270 → 90 FPSO + tanker bow 0.375 0.125 - continuous

2 217.5→180 FPSO + tanker bow 0.375 0.125 - step-by-step

3 270 → 90 FPSO + tanker bow 0.250 0.125 - continuous


5 270 → 90 FPSO + tanker bow 0.125 0.125 - continuous


3331 32 1 270 → 90 FPSO + tanker stern 0.125 0.125 - continuous

2 217.5→180 FPSO + tanker stern 0.125 0.125 - step-by-step3331 33 1 250 →120 FPSO + tanker stern 0.250 0.125 - continuous

2 217.5→180 FPSO + tanker stern 0.250 0.125 - step-by-step

3 240 →110 FPSO + tanker stern 0.375 0.125 - continuous

4 217.5→180 FPSO + tanker stern 0.375 0.125 - step-by-step




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Table 2 Position of the shuttle tanker (centre-line, left- and right side of the hull) in the

(model scale) co-ordinate system of the flow field measurements

ββββ= 195 ββββ= 210x

[m] yCL yleft yright yCL yleft yright

0.50 0.023 -0.054 0.101 0.006 -0.072 0.083

0.75 -0.044 -0.121 0.034 -0.139 -0.216 -0.061

1.00 -0.111 -0.188 -0.033 -0.283 -0.361 -0.205

1.25 -0.178 -0.255 -0.100 -0.427 -0.505 -0.350

1.50 -0.245 -0.322 -0.167 -0.572 -0.649 -0.494

x/c for ββββ= 195 x/c for ββββ= 210x

[m] pos I pos II pos III pos I pos II pos III

0.50 -0.021 -0.188 -0.354 0.007 -0.160 -0.326

0.75 0.324 0.157 -0.009 0.392 0.225 0.058

1.00 0.669 0.502 0.336 0.777 0.610 0.443

1.25 1.014 0.847 0.681 1.162 0.995 0.828

1.50 1.359 1.193 1.026 1.547 1.380 1.213 Note:

• yCL, yleft and yright are centre line, left- and right lateral wake intersect positions of the ship hull (in m at model

scale) in the flow field co-ordinate system (see Fig. 3)

• x/c denotes the intersect position along the ships centreline: x/c =0 at bow and x/c=1 at stern of the ship

Table 3 Average flow conditions over ship hull intersect area’s

β= 195 deg β= 210 degX [m]

ref 18 q/q ref 45q/q

18β∆ 45β∆ ref 18 q/q ref 45q/q

18β∆ 45β∆

0.50 0.280 0.400 -20.3 -10.3 0.167 0.272 -36.5 -13.3

0.75 0.373 0.579 -8.8 -3.0 0.313 0.430 -13.3 -4.0

1.00 0.485 0.640 -7.1 -2.5 0.631 0.780 -2.7 -1.1

1.25 0.553 0.687 -4.7 -1.5 0.793 0.924 -1.4 -0.8

1.5 0.623 0.756 -2.5 -0.8 - - - -

undisturbed 0.851 0.974 0.0 0.0 0.851 0.974 0.0 0.0 Note:

• )m18z(qq18 ==

• )m18z(18 =β∆=β∆




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Table 4 Average dynamic pressures and flow angles for each model segment.

Different model positions

pos 1 pos 2 pos 3

β= 195 bow middle stern bow middle stern bow middle stern

ref 18 q/q 0.33 0.43 0.52 0.38 0.48 0.55 0.43 0.52 0.58

ref 45 q/q 0.50 0.61 0.66 0.57 0.64 0.69 0.61 0.66 0.72

18β∆ -14.1 -7.9 -6.0 -9.9 -7.0 -4.8 -7.9 -6.0 -3.7

45β∆ -6.3 -2.7 -2.0 -3.8 -2.4 -1.6 -2.7 -2.0 -1.2

β= 210 bow middle stern bow middle stern bow middle sternref 18 q/q 0.23 0.41 0.65 0.30 0.54 0.72 0.41 0.65 0.80

ref 45 q/q 0.34 0.53 0.79 0.42 0.68 0.86 0.53 0.79 0.92

18β∆ -26.9 -10.6 -3.0 -17.5 -5.9 -1.9 -10.6 -3.0 -1.4

45β∆ -9.4 -3.3 -1.2 -5.8 -2.0 -0.9 -3.3 -1.2 -0.7

Note: Table cells for which ref q/q < 0.5 or β∆ > 5 degrees are shaded

Table 5 Forces and moments on the shuttle tanker depending on the mean wind velocity at10 m height (assuming a force and moment coefficient equal to unity)

V10

[m/s]Force[N]

Moment [Nm]

1 626 31320

2 2506 125280

4 10022 501120

6 22550 1127520

8 40090 2004480

10 62640 3132000

12 90202 4510080

14 122774 613872016 160358 8017920

18 202954 10147680

20 250560 12528000




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Fig. 1 Wake shielding test set-up in DNW-LST wind tunnel

a) side view

b) top view

Fig. 2 Sketch of the model dimensions (in [m]; full-scale) tested at 1:400 scale in DNW-LST wind tunnel

20

76 140

1410.5

26

22

18

300

upper-deck cargo (FPSO only)

604050




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Fig. 3 Position of the FPSO model with respect to tunnel centreline and wake traverse planes.Relative positions of shuttle tanker that were tested (see also Fig. 4) are shown for reference.

= -0.5 m

x= 0

∆x=0.25 m

∆y= 0.157 m

β= 210 deg

y

x

∆y= 0.028 m

β= 195 deg

y

x

= 0.5 m

wake traverse

planes




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Fig. 4 Sketch of the relative model positions (at full scale, in m)

50 50

50

50




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a) x= -0.50 m, β = 195 degrees

b) x= -0.25 m, β = 195 degrees

c) x= 0 m, β = 195 degrees




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g) x= 1.00 m, β = 195 degrees

h) x= 1.25 m, β = 195 degrees

i) x= 1.50 m, β = 195 degrees

Fig. 5 Measured flow fields behind FPSO, wind heading β = 195 degrees




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a) x= -0.50 m, β = 210 degrees

b) x= -0.25 m, β = 210 degrees

c) x= 0 m, β = 210 degrees




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d) x= 0.25 m, β = 210 degrees

e) x= 0.50 m, β = 210 degrees

f) x= 0.75 m, β = 210 degrees




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g) x= 1.00 m, β = 210 degrees

h) x= 1.25 m, β = 210 degrees

i) x= 1.50 m, β = 210 degrees

Fig. 6 Measured flow fields behind FPSO, wind heading β = 210 degrees




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ββββ = 195

0

10

20

30

40

50

60

70

80

90

100

-30 -25 -20 -15 -10 -5 0

∆∆∆∆ββββ avg [deg]

z [m] x=0.50

x=0.75

x=1.00

x=1.25

x=1.50

b) ∆ )z(β

ββββ= 195

0

10

20

30

40

50

60

70

80

90

100

0.0 0.2 0.4 0.6 0.8 1.0 1.2

q/qref

z [ m ]

x=0.50

x=0.75

x=1.00

x=1.25

x=1.50seaprof

c) q(z)/qref

ββββ= 195

0

10

20

30

40

50

60

70

80

90

100

0.0 0.2 0.4 0.6 0.8 1.0 1.2

qavg /qref,

z [m]x=0.50

x=0.75

x=1.00

x=1.25

x=1.50

seaprof

d) ref q/)z(q

Fig. 8 Averaged profile data (averaged between y min and y max values given in Tab. 2), β =195




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ββββ= 210

0

10

20

30

40

50

60

70

80

90

100

-50 -40 -30 -20 -10 0 10

∆∆∆∆ββββ [deg]

z [m]x=0.50

x=0.75

x=1.00

x=1.25

a) ∆β(z)

ββββ= 210

0

10

20

30

40

50

60

70

80

90

100

-50 -40 -30 -20 -10 0

∆∆∆∆ββββavg [deg]

z [m]x=0.50

x=0.75

x=1.00

x=1.25

b) ∆ )z(β

ββββ= 210

0

10

20

30

40

50

6070

80

90

100

0.0 0.2 0.4 0.6 0.8 1.0 1.2

q/qref

z [ m ] x=0.50

x=0.75

x=1.00

x=1.25

x=-0.5

c) q(z)/qref




-42-

NLR-CR-2003-018


ββββ= 210

0

10

20

30

40

50

60

70

80

90

100

0.0 0.2 0.4 0.6 0.8 1.0 1.2

qavg /qref

z [m] x=0.50

x=0.75

x=1.00

x=1.25

x=-0.5

d) ref q/)z(q

Fig. 9 Averaged profile data (averaged between y min and y max values given in Tab. 2), β =210

ββββ= 195 [deg]

-30

-25

-20

-15

-10

-5

0

-0.5 0 0.5 1 1.5

x/c

1 8 , a v g

[ d e g ]

pos 1

pos 2

pos 3

a) ∆ 18β

ββββ= 195 [deg]

-30

-25

-20

-15

-10

-5

0

-0.5 0 0.5 1 1.5

x/c

4 5 , a v g

[ d e g ]

pos 1

pos 2

pos 3

b) ∆ 45β




-43-

NLR-CR-2003-018


ββββ= 195 [deg]

0

0.2

0.4

0.6

0.8

1

-0.5 0 0.5 1 1.5

x/c

q 1 8 , a v g

/ q r e f pos 1

pos 2

pos 3

undisturbed

c ) 18q /qref

ββββ= 195 [deg]

0

0.2

0.4

0.6

0.8

1

-0.5 0 0.5 1 1.5

x/c

q 4 5 , a v g

/ q r e f pos 1

pos 2

pos 3

undisturbed

d) 45q /qref

Fig. 10 Flow direction and average dynamic pressure along the ship hull for various positions

of the offloading tanker ( β =195)




-44-

NLR-CR-2003-018


ββββ= 210 [deg]

-30

-25

-20

-15

-10

-5

0

-0.5 0 0.5 1 1.5

x/c

1 8 , a v g

[ d e g ]

pos 1

pos 2

pos 3

a) ∆ 18β

ββββ= 210 [deg]

-30

-25

-20

-15

-10

-5

0

-0.5 0 0.5 1 1.5

x/c

4 5 , a v g

[ d e g ]

pos 1

pos 2

pos 3

b) ∆ 45β

ββββ= 210 [deg]

0

0.2

0.4

0.6

0.8

1

-0.5 0 0.5 1 1.5

x/c

q 1 8 , a v g

/ q r e f pos 1

pos 2

pos 3

undisturbed

c ) 18q /qref




-46-

NLR-CR-2003-018


Fig. 12 Definition of wind headings relative to the FPSO vessel

Fig. 13 Force and moment sign conventions for the shuttle tanker (right-handed co-ordinate system)

Fig. 14 Segmentation of the off-loading shuttle tanker

0 degrees

270 degrees

90 degrees

180 degrees

x

y

Fx

Fy

Fz

Mx

My

Mz

Fx Mz

Fy

bowmiddlestern

Mz

Fy

Mz

Fy

Fx Fx

DL

V




-47-

NLR-CR-2003-018


Forces and moments on the ship hull Forces and moment contributions fromthe steering house

Fig. 15 Sketch of the flow pattern and force and moment contributions of the hull and steering house

CD

CL=0CM z=0

-

+

-

= 0 de

CL

CD

CM,z<0

-

+

= 20de

CD

CL≈ 0

CM,z≈ 0

-

+

-

= 90 de

CD

CL

CM z>0

+

+

-

= 160 de

-

+

+

CL

CD

CM,z<0

β= 200 deg

∆CD

∆CM z

∆CM z

∆CD

∆CD

∆CL

∆CD

∆CM z

∆CD

∆CL

∆CM z




-48-

NLR-CR-2003-018


-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

Cz

Cx

Cy

Fig. 16 Force coefficients C x , C y , C z as function of wind heading (no wind shielding)

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CL

CD

Fig. 17 Flow oriented drag and side-force coefficients C D and C L as function of wind heading (no wind shielding)




-50-

NLR-CR-2003-018


-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CMy

CMz

CMx

Fig. 19 Moment coefficients C M,x , C M,y , C M,z as function of wind heading (moments on total model; no wind shielding)

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0 30 60 90 120 150 180 210 240 270 300 330 360

β [deg]

d Mx

d My

d Mz

Fig. 20 Force “ application” distances d M,x , d M,y , d M,z (referenced to the ships hull length)computed with equation 5 (no wind shielding)




-51-

NLR-CR-2003-018


-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

150 180 210 240 270 300 330 360

ββββ [deg]

Cz: summed

Cx: summed

Cy: summed

Cz: total

Cx: total

Cy: total

Fig. 21 Consistency check of step-by-step force measurement data.(no wind shielding). Linesrepresent measurements of forces on total ship geometry, symbols represent sum of forces measured for the different model segments (see equation 6)

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

150 180 210 240 270 300 330 360

ββββ [deg]

CMz: summed

CMx: summed

CMy: summed

CMz: total

CMx: total

CMy: total

Fig. 22 Consistency check of step-by-step moment measurement data (no wind shielding).Lines represent measurement of moments on total ship geometry, symbols represent summed data for the different model segments (see equation 6)




-52-

NLR-CR-2003-018


-0.20

-0.10

0.00

0.10

0.20

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

Cx

bow

middle

stern

Fig. 23 Contributions of the different model segments to C x (no wind-shielding)

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

Cy

bow

middle

stern

Fig. 24 Contributions of the different model segments to C y (no wind-shielding)

-0.10

0.00

0.10

0.20

0.30

0.40

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

Cz

bow

middle

stern

Fig. 25 Contributions of the different model segments to C z (no wind-shielding)




-53-

NLR-CR-2003-018


-0.10

0.00

0.10

0.20

0.30

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CD

bow

middle

stern

Fig. 26 Contributions of the different model segments to C D (no wind-shielding)

-0.20

-0.10

0.00

0.10

0.20

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CL

bow

middle

stern

Fig. 27 Contributions of the different model segments to C L (no wind-shielding)




-54-

NLR-CR-2003-018


-0.20

-0.10

0.00

0.10

0.20

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,x

bow

middle

stern

Fig. 28 Contributions of the different model segments to C M,x (no wind-shielding)

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,y

bow

middle

stern

Fig. 29 Contributions of the different model segments to C M,y (no wind-shielding)

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.400.60

0.80

1.00

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,z

bow

middle

stern

Fig. 30 Contributions of the different model segments to C M,z (no wind-shielding)




-57-

NLR-CR-2003-018


-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,x

unshielded

x=0.125

x=0.250

x=0.375

a) C M,x

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,y

unshielded

x=0.125

x=0.250

x=0.375

b) C M,y

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,z

unshielded

x=0.125

x=0.250

x=0.375

b) C M,z

Fig. 33 Effect of wind shielding on moment coefficients C M,x , C M,y and C M,z as function of wind heading and model position




-58-

NLR-CR-2003-018


-0.20

-0.10

0.00

0.10

0.20

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

Cx

unshielded

x=0.125

x=0.250

x=0.375

a) bow segment

-0.20

-0.10

0.00

0.10

0.20

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

Cx

unshielded

x=0.125

x=0.250

x=0.375

b) middle segment

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

Cx

unshielded

x=0.125

x=0.250

x=0.375

c) stern segment

Fig. 34 Wind shielding effects on C x . Contributions of the different model segments




-59-

NLR-CR-2003-018


-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

Cy

unshielded

x=0.125

x=0.250

x=0.375

a) bow segment

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

Cy

unshielded

x=0.125

x=0.250

x=0.375

b) middle segment

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

Cy

unshieldedx=0.125

x=0.250

x=0.375

c) stern segment

Fig. 35 Wind shielding effects on C y . Contributions of the different model segments




-62-

NLR-CR-2003-018


-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,y

unshielded

x=0.125

x=0.250

x=0.375

a) bow segment

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,y

unshielded

x=0.125

x=0.250

x=0.375

b) middle segment

-1.00

-0.80

-0.60

-0.40

-0.20

0.000.20

0.40

0.60

0.80

1.00

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,y

unshieldedx=0.125

x=0.250

x=0.375

c) stern segment

Fig. 38 Wind shielding effects on C M,y . Contributions of the different model segments




-63-

NLR-CR-2003-018


-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,z

unshielded

x=0.125

x=0.250

x=0.375

a) bow segment

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,z

unshielded

x=0.125

x=0.250

x=0.375

b) middle segment

-1.00

-0.80

-0.60

-0.40

-0.20

0.000.20

0.40

0.60

0.80

1.00

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CM,z

unshieldedx=0.125

x=0.250

x=0.375

c) stern segment

Fig. 39 Wind shielding effects on C M,z . Contributions of the different model segments




-64-

NLR-CR-2003-018


a) “Large” distance between the two tankers. Negligible influence of shuttle tanker on the flow

conditions at the FPSO. Global flow conditions at some distance upstream of the shuttle

tanker are not different than for the case without shuttle tanker. Frozen velocity field

assumption is valid.

b) “Medium” distance between the tankers. Some influence of the shuttle tanker on the flow

conditions at and the forces on the FPSO. Global flow conditions behind the FPSO are

somewhat different than for a case without shuttle tanker. Frozen velocity field approximation

is weakly violated.

c) “short” distance between the tankers. Strong influence of the shuttle tanker on the FPSO,

direct coupling between the flow fields around FPSO and shuttle tanker. Frozen velocity field

assumption is violated.

Fig. 40 Sketch (very schematic) of the interaction effect between two tankers in relation totheir relative distance d (assuming that the FPSO is upstream of the shuttle tanker)

FPSO tanker d

shuttle tanker

FPSO tanker d

shuttle tanker

FPSO tanker

d

shuttle tanker




-65-

NLR-CR-2003-018


bow (ββββ=195)

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.000 0.1 0.2 0.3 0.4

model position x [m]

Cx

unshielded

shielded

calc. (beta)

calc. (beta, q)

middle (ββββ=195)

0.00

0.01

0.02

0.03

0 0.1 0.2 0.3 0.4


Cx

unshielded

shielded

calc. (beta)

calc. (beta, q)

stern (ββββ=195)

-0.20

-0.15

-0.10

-0.05

0.00

0 0.1 0.2 0.3 0.4


Cx

unshielded

shielded

calc. (beta)

calc. (beta, q)

total ( ββββ=195)

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0 0.1 0.2 0.3 0.4


Cx

unshielded

shielded

unshield (sum)

shielded (sum)

calc. (beta, q)

Fig. 41 Wind shielding correction for each model segment (C x , β = 195 degrees)




-67-

NLR-CR-2003-018


bow (ββββ=195)

-0.20

-0.15

-0.10

-0.05

0.000 0.1 0.2 0.3 0.4


C

M,z

unshielded

shielded

calc. (beta)

calc. (beta, q)


-0.01

0.00

0.01

0 0.1 0.2 0.3 0.4


C

M,z

unshielded

shielded

calc. (beta)

calc. (beta, q)

stern ( ββββ=195)

0.00

0.02

0.04

0.06

0.08

0.10

0 0.1 0.2 0.3 0.4


∆∆∆∆C

M,z

unshielded

shielded

calc. (beta)

calc. (beta, q)


-0.10

0.00

0.10

0.20

0 0.1 0.2 0.3 0.4


C

M,z

unshielded

shielded

unshield (sum)

shielded (sum)

calc. (beta, q)

Fig. 43 Wind shielding correction for each model segment (C M,z , β = 195 degrees)




-68-

NLR-CR-2003-018


bow (ββββ=210)

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.000 0.1 0.2 0.3 0.4


Cx

unshielded

shielded

calc. (beta)

calc. (beta, q)


0.00

0.01

0.02

0.03

0 0.1 0.2 0.3 0.4


Cx

unshielded

shielded

calc. (beta)

calc. (beta, q)


-0.20

-0.15

-0.10

-0.05

0.00

0 0.1 0.2 0.3 0.4


Cx

unshielded

shielded

calc. (beta)

calc. (beta, q)


-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0 0.1 0.2 0.3 0.4


Cx

unshielded

shielded

unshield (sum)

shielded (sum)

calc. (beta, q)

Fig. 44 Wind shielding correction for each model segment (C x , β = 210 degrees)




-69-

NLR-CR-2003-018


bow (ββββ=210)

-0.10

-0.08

-0.06

-0.04

-0.02

0.000 0.1 0.2 0.3 0.4


Cy

unshielded

shielded

calc. (beta)

calc. (beta, q)


-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0 0.1 0.2 0.3 0.4


C

unshielded

shielded

calc. (beta)

calc. (beta, q)


-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0 0.1 0.2 0.3 0.4


C

unshielded

shielded

calc. (beta)

calc. (beta, q)


-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0 0.1 0.2 0.3 0.4


C

unshielded

shielded

unshield (sum)

shielded (sum)

calc. (beta, q)

Fig. 45 Wind shielding correction for each model segment (C y , β = 210 degrees)




-70-

NLR-CR-2003-018


bow (ββββ=210)

-0.40

-0.30

-0.20

-0.10

0.000 0.1 0.2 0.3 0.4


C

M,z

unshielded

shielded

calc. (beta)

calc. (beta, q)


-0.01

0.00

0.01

0.02

0 0.1 0.2 0.3 0.4


C

M,z

unshielded

shielded

calc. (beta)

calc. (beta, q)

stern ( ββββ=210)

0.00

0.10

0.20

0.30

0.40

0 0.1 0.2 0.3 0.4


C

M,z

unshielded

shielded

calc. (beta)

calc. (beta, q)


-0.10

0.00

0.10

0.20

0.30

0.40

0 0.1 0.2 0.3 0.4


C

M,z

unshielded

shielded

unshield (sum)

shielded (sum)

calc. (beta, q)

Fig. 46 Wind shielding correction for each model segment (C M,z , β = 210 degrees)




-71-

NLR-CR-2003-018


Fig. 47 Summary of wind shielding calculation results

-0.25

-0.20

-0.15

-0.10

180 190 200 210 220

ββββ [deg]

Cx

unshielded (total)

shielded (x=0.125, total)



calc. (x=.125, summed)calc. (x=.250, summed)

calc. (x=.375, summed)

unshielded (summed)

shielded (x=.125, summed)



-0.25

-0.20

-0.15

-0.10

-0.05

0.00

180 190 200 210 220

ββββ [deg]

Cy

unshielded (total)







unshielded (summed)




-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

180 190 200 210 220

ββββ [deg]

CM,z

unshielded (total)shielded (x=0.125, total)

shielded (x=0.250, total)shielded (x=0.375, total)


calc. (x=.250, summed)calc. (x=.375, summed)

unshielded (summed)

shielded (x=.125, summed)shielded (x=.250, summed)





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NLR-CR-2003-018


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-73-

NLR-CR-2003-018


Appendix A Drag coefficient of the shuttle tanker when based on the frontal wind

exposed area

In traditional force models, see e.g. references 4-6, the drag is found by summing the drag

contributions of the different model segments. For the individual model segments drag is

computed by multiplying the drag coefficient with the projected wind-exposed area of the

model segment with the mean dynamic wind pressure over the height of the model segment. For

sharp edged geometry elements a drag coefficient in the order of one should be expected for all

model elements.

It was checked if with a drag coefficient definition based on the frontal exposed area of the

shuttle tanker a more constant drag coefficient would have been obtained. The ship geometry

(see Fig. 2) was approximated with three prismatic elements:

1) The ships hull (300x50x18 m3).

2) The lower part of the steering house (26x40x22 m3 ).

3) The upper part of the steering house (highly schematised: 8x65x5 m3 ).

Wind velocity (relative to the wind velocity at the reference height of 52 m) and dynamic wind

pressure profiles (referenced to the average dynamic wind pressure between z=0 and z=52 m:

qref ) are shown in figure A.1, together with a backside view of the ship. Dynamic wind pressures

were averaged over the height of the model parts and the results are given in table A.1. Theseresults were applied to obtain an effective drag coefficient

*

DC based on the projected frontal

area of the ship and the effective dynamic pressures of the three main model parts (1: main ship

hull, 2: lower part of the steering house, 3: upper part of the steering house). The following

formula’s were used:

( )

++

=⇒

++==

ref

3

ref

3

ref

2

ref

2

ref

1

ref

1

D*

D

332211

*

Dref ref D

A

A

q

q

A

A

q

q

A

A

q

q

CC

AqAqAqCAqCD

The following formulas for the frontal area of the model parts apply:

[ ]

[ ]

[ ]))8/65(sin(tan(abs),)8/65((sin(tanabsmax8655A

,))26/40(sin(tan(abs),)26/40((sin(tanabsmax264022A

,))300/50(tan(sin(abs),)300/50((sin(tanabsmax3005018A

1122

3

1122

2

1122

1

β+−β++=

β+−β++=

β+−β++=

−−

−−

−−




-74-

NLR-CR-2003-018


The result, shown in figure A.2, shows a*

DC value around 0.75. Compared to the original drag

coefficient definition (based on a constant reference area, see equations 2 and 3 and Fig. 17) the

maximum deviations are now smaller: in the order of about 20% depending on flow angle β.

Table A.1 Average dynamic wind pressures over the height of the main model parts

(from equation 1, with α=0.1)

model part zmin [m] zmax [m] ref q/q [-]

hull 0 18 0.809

steering house lower part (stern-1) 18 40 1.063

steering house upper part (stern-2) 40 45 1.152

lower bow part (bow-1) 18 22 0.991

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1 1.2 1.4

z [m] V/Vref

q/qref

a) wind and dynamic wind pressure profile b) ship geometry (view from the back)

Fig. A.1 Simulated wind profile with respect to the model geometry




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Appendix B Application of slender wing theory for deriving an empirical formula

for the side force coefficient CL

The variation of the side force coefficient CL with β is shown in figure 17. For small flow angles

there is a slow increment of CL with β, followed by a much more rapid increment at larger flow

angles. Since this behaviour is well known from slender wing theory and the hull of the ship

resembles to some extend a slender wing, it is useful to see if elements of slender wing theory

can be used to describe the observed variation of CL with β.

The sea surface can be considered as a symmetry plane. The ship’s hull then resembles a “wing”

with a chord c of 300 m and a span b of 2 times the height of the hull (2 x 18= 36 m). The

aspect ratio A of that wing is equal to b2/(bc)= 0.12. According to references 7-8 the lift

coefficient (here that lift force is actually a side force) of a slender infinitely thin (flat plate)

wing in a uniform flow can be approximated as:

)sinA(cossin5.0CL β+ββπ= (Eq. B.1)

As argued in reference 7, the factor 0.5π is in fact to be expected lower because the effective

hull geometry is not a flat plate, but has a rectangular (36 x 60 m2) cross-section. Apart from

this, the basic formulation should still apply, albeit the lift of the ship’s hull would only be half the value of the lift on the equivalent slender wing. From equation B-1 the lift coefficient of the

ship hull, referenced to qref rather than q 18 (the average dynamic pressure over the height of the

ship’s hull) and to Aref rather than S= bc, and with an empirical reduction factor p becomes:

}360,180,min{

)q/q()A/S()sinA(cossin p25.0C

*

ref 18ref

*

L

β−β−β=β

β+ββπ=(Eq. B.2)

This result is compared against the measurements in Figure B-1. With p equal to unity the

model predicts lift in qualitative agreement with the measurements, but the predicted lift is

much too large. With p adapted to the experimental data (p=0.35 for 90<β and p=0.5 for

90>β ) a quite reasonable agreement is found. However, the linear lift gradient is still too

large near β= 180 (flow from the bow) and still much too large near β= 0 degrees (flow from the

stern).




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-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0 30 60 90 120 150 180 210 240 270 300 330 360

ββββ [deg]

CL

measured

Eq. B-1, p=1Eq. B-2, p adapted

Fig. B.1 Measured C L and calculated C L with modified slender wing theory (equation B.1), nowind shielding

p= 0.35 p= 0.50 p= 0.35




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For each part CD is computed with equation C.2.'

xC is a function of H/b and a/b; k l is the

turbulent length-scale effect and a function of the ratio between a and the longitudinal

turbulence length scale xLU; k i depends on turbulence intensity Iu and on a/b and H/b. Data of

reference 6 have been used. Magnitude of k i is unclear because H/b of ships hull is outside

empirical data range. Therefore two values for k i have been employed.

This has also been computed in table C.1. It has to be noted that the computed forces and

moments are larger than the experimental values. Even when k i = 1 is taken.

It is concluded that the experimental data do not fit well with the method presented in reference

6. This might partly be due to uncertainties in the turbulence parameters and to the fact that theships hull height is small (H/b of the hull lies outside the empirical data range, especially for the

β=90 degree case). A further drawback of the method presented in Ref.6 is that it does not give

sufficiently detailed data on k β in relation to the a/b and H/b ratio.

1174399573640-JIP Shielding Model Final

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