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Title:
FLOATING UNIT AND A METHOD FOR REDUCING HEAVE AND PITCH/ROLL MOTIONS OF A FLOATING UNIT
Document Type and Number:
WIPO Patent Application WO/2014/108432
Kind Code:
A1
Abstract:
A floating unit (10) is disclosed comprising a single centre barrel (11) having a longitudinal centre axis (22). The central barrel comprises a lower main section (14) and an upper section (12) extending up from the main section (14) and having at least one outward facing side (20) which forms a flare angle (φ) with the longitudinal axis (22). The upper section (12) penetrates a still water surface (30) when the floating unit is in use. The main section (14) of the floating structure (10) has an equivalent diameter (D), a still water draught (T) and a metacentric height (KM) which is given as a function of the diameter (D), the still water draught (T), the flare angle (φ) and a variable part (x) of the draught which is a result of the motions of the floating unit (10) such that KM = ΚΜ(D,Τ,φ,x). The flare angle (φ) of the upper section ( 12 ) is within a range of ±20% of the flare angle φ which satisfies the equation d(KM(D,T,φ,x))/dx = 0.

Inventors:
PETTERSEN ERIK (NO)
HANSSEN FINN-CHRISTIAN WICKMANN (NO)
Application Number:
PCT/EP2014/050208
Publication Date:
July 17, 2014
Filing Date:
January 08, 2014
Export Citation:
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Assignee:
MOSS MARITIME AS (NO)
International Classes:
B63B9/08; B63B1/04; B63B22/24; B63B22/26; B63B35/08; B63B39/10
Domestic Patent References:
WO2009136799A12009-11-12
WO2011056695A12011-05-12
WO2002090177A12002-11-14
Foreign References:
US6761508B12004-07-13
US4434741A1984-03-06
US20120298027A12012-11-29
Attorney, Agent or Firm:
ONSAGERS AS (Oslo, NO)
Download PDF:
Claims:
CLAIMS

1. A floating unit (10) comprising a single centre barrel (11) having a longitudinal centre axis (22), the central barrel comprising a lower main section (14) and an upper section (12) extending up from the main section (14) and having at least one outward facing side (13) which forms a flare angle (φ) with a vertical axis

(22) and wherein the upper section (12) penetrates a still water surface (30) when the floating unit is in use, the main section (14) of the floating structure (10) further having an equivalent diameter (D), a still water draught (T) and a metacentric height (KM) which is given as a function of the diameter (D), the still water draught (T), the flare angle (φ) and a variable part (x) of the draught which is a result of the motions of the floating unit (10) such that

KM = ΚΜ(ϋ,Τ,φ,χ), wherein the flare angle (φ) of the upper section (12) is within a range of ±20% of the optimal flare angle (φ) which satisfies the equation d(KM(D,T,cp,x))/dx = 0

2. Floating unit according to claim 1,

c h ar ac te ri ze d i n that the upper section (12), as seen in a side view, is conically shaped.

Floating unit according to claim 1,

c h ar act e ri z e d in that the upper section (12), as seen in a side view, has a curved shape.

Floating unit according to one of the claims 1-3,

c har ac t e r i z e d i n that a horizontal cross section of the barrel (11) of the floating structure (10), perpendicular to the longitudinal axis (22) of the of the floating structure (10), has a regular polygonal shape.

Floating unit according to one of the claims 1 -4,

c h ar act e ri z e d i n that a horizontal cross section of the barrel (11) of the floating structure (10), perpendicular to the longitudinal axis (22) of the of the floating structure (10), has a regular octagonal shape.

Floating unit according to one of the claims 1-3,

c har ac t e r i z e d i n that a horizontal cross section of the barrel (11) of the floating structure (10), perpendicular to the longitudinal axis (22) of the of the floating structure (10), is circular.

A method for reducing pitch/roll motions of a single centre barrel floating unit (10) comprising a single centre barrel (11) having a longitudinal centre axis (22), the central barrel comprising a lower main section (14) and an upper section (12) extending up from the main section (14) and having at least one outward facing side (20) which forms a flare angle (φ) with the longitudinal axis (22) and wherein the upper section (12) penetrates a still water surface (30) when the floating unit is in use, the main section (14) of the floating structure

(10) further having an equivalent diameter (D), a still water draught (T) and a metacentric height (KM) which is given as a function of the diameter (D), the still water draught (T), the flare angle (φ) and a variable part (x) of the draught which is a result of the motions of the floating unit (10) such that

KM = ΚΜ(ϋ,Τ,φ,χ), wherein the flare angle (φ) of the upper section (12) is chosen such that it is within a range of ±20% of the optimal flare angle (φ) which satisfies the equation d(KM(D,T,cp,x))/dx = 0

Description:
Floating unit and a method for reducing heave and pitch/roll motions of a floating unit

The present invention relates to improving the motion characteristics of a single barrel floating unit. It has been observed that this type of floating units can be subjected to excessive roll/pitch motions in some sea conditions. Similar designs of floating units try to eliminate such motions by providing as much damping as possible to the floating unit.

Single barrel floating structures have previously been described, for example in the published PCT-application WO 02/090177 Al and the published US patent application No. 2012/0298027 Al. In the US-publication there is disclosed a floating structure for use in ice-covered water comprising a single barrel hull which is designed to decrease ice loads and provide more ice breaking mechanisms than conventional vessel structures. The floating vessel is provided with a conically shaped part and an uneven sided polygonal shape of the hull in order to break the ice more efficiently. Pitch/roll, heave and surge motions are induced by shifting ballast water in the ballast tanks, thereby breaking the ice more efficiently.

The objective of the claimed invention is to reduce roll/pitch motions of a single barrel floating unit in the sea. A further objective of the present invention has been to increase the damping of a single barrel floating unit and simultaneously simplify the manufacturing process of such a floating unit.

These objectives are achieved with a floating unit as defined in claim 1 and method as defined in claim 7. Further embodiments of the floating unit are defined in the dependent claims 2-6.

The strategy when developing the claimed invention was to find a way to reduce unwanted motions by changing the shape of the floating unit rather than increasing the damping. The floating structure may of course be provided with means for damping as much as possible in addition. The reason for motions that are experienced but that cannot be explained by linear theory is probably parametric coupling between various motion components, so- called Mathieu motions. The conditions causing this behaviour can be described by a differential equation which has a solution in some regions, while in other regions it is unstable and the solution will diverge to infinity. The Mathieu differential equation may be written:

?j + S7 2 (1— Ξ COS 6> 3 t)f?— 0 wherein ε is the relative size of this variation in the stiffness term and n is the ratio between the natural frequency and the stiffness frequency. The equation shows that the "stiffness" term has a regular variation with a frequency that may be different from the eigen-frequency of the system. The relative size of this variation in the stiffness term (ε) and the ratio between the natural frequency and the stiffness frequency (TIT) are then governing for the solution.

In Figure 1 the areas of stable and unstable solutions of the equation are shown. As can be seen from Figure 1, a ratio of τσ = 0.5 results in the largest instability, but τπ = 1, 1.5 and 2 can also result in instabilities. The size of the stiffness variation (ε) also plays a role in that increasing the stiffness variation will increase the instability region.

The claimed invention is a barrel type floating unit, preferably with an octagonal cross section, but may also be given other shapes, for example circular. The floating unit can also be provided with an internal moonpool. The floating unit is characterized by the average diameter (D) and draught (T). If the claimed invention is designed as an octagon with eight plane side panels, the diameter is defined as the inscribed circle in the octagon. If other polygonal shapes are chosen, the diameter will correspondingly be defined as the inscribed circle in the polygon. An octagonal shape results in increased viscous damping obtained by sharp corners and simplified production since plane steel panels are much easier to produce than curved panels.

For a floating unit such as the claimed invention, the differential equation above may represent the pitch/roll motion, and the stiffness variation may be represented by the variation of the metacentric height (GM) caused by heave motions.

The frequency of the heave motions is governed by the natural period in heave, or simply the wave excitation frequency. With for instance a heave excitation period of 12 seconds and a natural period in roll of 24 seconds, the frequency ratio will be w = 0.5 and the possibility of entering into the unstable region is very high as shown in Figure 1. If the heave natural period and the wave excitation are coinciding, this will of course magnify the problem.

Previously, as mentioned above, to avoid excessive pitch/roll motions, i.e. to enter the unstable regions shown in Figure 1 , floating units have been provided with as much damping as possible. Another option to avoid entering the unstable region would be to prevent the frequency ratio to enter into the unstable regions. However, considering the fact that the excitation comes from a stochastic process (the waves), it will be very difficult to prevent the frequency ratio to enter into the dangerous regions. As a further alternative, the inventor has therefore contemplated a third possibility to avoid the possibility of entering into the unstable regions, which is to reduce the variation of the stiffness GM (ε in Figure 1) as much as possible. This would seem to be the most effective way to reduce the exposure to Mathieu instability.

A floating unit is disclosed comprising a single centre barrel having a longitudinal centre axis. The central barrel comprises a lower main section and an upper section extending up from the main section and having at least one outward facing side, i.e. facing away from the interior of the floating unit and towards the surroundings, which forms a flare angle (φ) with a vertical axis. The upper section penetrates a still water surface when the floating unit is in use. The main section of the floating structure further has an equivalent diameter (D), a still water draught (T) and a metacentric height (KM) which is given as a function of the diameter (D), the still water draught (T), the flare angle (φ) and a variable part (x) of the draught which is a result of the motions of the floating unit such that KM = ΚΜ(ϋ,Τ,φ,χ). The flare angle (φ) of the upper section is within a range of ±20% of the optimal flare angle (φ) which satisfies the equation d(KM(D,T,9,x))/dx = 0

Alternatively, this may be expressed such that the optimal flare angle (φ) of the upper section (12) is the angle which satisfies the equation d(KM(D,T,cp,x))/dx = 0 and wherein the flare angle of the upper section is within the range of ±20% of the optimal flare angle.

When the upper section is provided with such a flare angle, the parametric connection between heave and pitch/roll will be decoupled.

The upper section, as seen in a side view, may be conically shaped or alternatively the upper section, as seen in a side view, may have a curved shape.

A horizontal cross section of the barrel of the floating structure, perpendicular to the longitudinal axis of the floating structure, may have a regular polygonal shape, for example a regular octagonal shape. Alternatively the horizontal cross section of the barrel of the floating structure, perpendicular to the longitudinal axis of the of the floating structure may be circular. A method for reducing pitch/roll motions of a single centre barrel floating uni is also disclosed wherein the floating structure comprises a single centre barrel having a longitudinal centre axis. The central barrel comprises a lower main section and an upper section extending up from the main section and having at least one outward facing side, i.e. facing away from the interior of the floating unit and towards the surroundings, which forms a flare angle (φ) with a vertical axis. The upper section penetrates a still water surface when the floating unit is in use. The main section of the floating structure further has an equivalent diameter (D), a still water draught (T) and a metacentric height (KM) which is given as a function of the diameter (D), the still water draught (T), the flare angle (φ) and a variable part (x) of the draught which is a result of the motions of the floating unit (10) such that

KM = ΚΜ(ϋ,Τ,φ,χ). The flare angle (φ) of the upper section (12) is chosen such that it is within a range of ±20% of the optimal flare angle (φ) which satisfies the equation d(KM(D,T.(p.x ))/dx = 0

The equivalent diameter (D) mentioned several times above is equal to the actual diameter if the main section has a circular cross section. If the cross section of the main section is polygonal, the equivalent diameter (D) is taken as the diameter of the circle which gives the same area as the area of the actual polygonal cross section.

A non-limiting embodiment of the present invention will now be further described with reference to the figures where

Figure 1 is discussed above and shows the stability diagram for Mathieu's equation.

Figure 2 shows KM as a function of Draught for various diameters D. Figure 3 shows the derivative of the KM-function as a function of draught (T) for various diameters.

Figure 4 shows a graph showing D-T combinations where the derivative of KM is equal to 0.

Figure 5 shows a plot where 6KM(D,T, φ,χ) is plotted for several angles as a function of the draught (T).

Figure 6 shows a plot of the flare angle that will give no variation of the metacentric height.

Figure 7 shows a side view of a floating unit according to the present invention. Figure 8 shows a cross section of the floating unit shown in Figure 7.

Figure 9 shows an embodiment of the present invention with flare.

We will in the following discuss how a design according to the claimed invention may enter into the Mathieu instability region and how the claimed invention solves this problem.

As mentioned, the claimed invention is a single barrel shaped design, where the cross section preferably is in the shape of an octagon, but may also be circular or generally in the shape of a regular polygon.

The octagonal or polygonal shape is not relevant for the considerations related to the present invention, so we will in the mathematical expressions below assume that the claimed invention has a circular cross section with diameter D and draught T. The diameter may be selected such that π/4*ϋ 2 will give the same cross sectional area as the octagon of the actual floating unit under consideration.

A circular barrel comprising a main section with a constant cross section as function of height will therefore be considered.

The metacentric height, which is the distance from the keel to the metacenter KM, may be written:

KM = KB + BM where KB is the distance from the keel to the center of buoyancy and BM is the metacentric height which is the distance from the center of buoyancy to the metacenter.

BM is given by the following expression: BM=I/V where I is the moment of inertia of the water plane area, i.e. for a circular water line which means that I = π/64*ϋ 4 , and V is the displacement, i.e. V = π/2*02 *T.

Simplifying the expression, BM can be written:

KM = T/2 + D 2 /(16*T)

This expression can be differentiated with respect to T. The following is then obtained: d(KM)/dT = ½ - D 2 /(16*T 2 ) The draught T giving no variation of the BM is: d(KM)/dT = 0 => ½-l/16*(D/T) 2 = 0 Solving this equation for D/T: D/T = (8) 1/2 A plot of the metacentric parameter KM as function of D is shown in Figure 2.

Note that variations in KM will equal variations in GM, since GM = KM - KG and KG remains constant for a given loading condition.

A plot of the derivative of KM with respect to the draught T, i.e.

d(KM)/dT = ½-D 2 /(16*T 2 ), is shown in Figure 3. In fi gure 3, the variation of KM is plotted for several diameters as a function of the draught T.

As an example, a floating unit with a diameter of 90 m is chosen herein, but a floating unit having a different diameter D will obviously be having different results.

For a draught of 31m, the value is equal to zero (i.e. δΚΜ(Τ,90) = 0 in Figure 3). For smaller draughts, the variation gets larger and larger numerical values. It is clear that for draughts well below 30 m, the condition for getting Mathieu instability is present since the parameter ε becomes a significant number.

Figure 3 also shows that for each diameter, there is a draught (T) which gives zero value of the variation of KM. This relation is shown in Figure 4 where the line is based on both a numerical solution of δΚΜ = 0 and the equation D/T = (8) 1/2 , both giving the same result.

It is, however, not always possible to design a floating unit with D-T combinations as shown above. A diameter of for instance 90m requires a draught of about 31 m. In many situations, this is not possible, but a draught of say 20 m will result in a situation where the KM value will have a variation by dynamic variation of draught. How to solve this problem will now be explained in detail.

In figures 7-9 there is shown an embodiment of the claimed floating unit 10 with a single centre barrel 1 1 which supports a deck structure 16. The centre barrel 1 1 comprises a cylindrical main section 14 with a octogonally shaped cross section and a conically shaped upper section 12 which extends from the top of the main section and through the water surface 30 o still water. The upper section 12 comprises outward facing sides 13 which face the surroundings. On top of the upper section 12 the floating unit is provided with the deck structure 16. Normally the outward facing sides 13 of the conically shaped upper section 12 will be inclined outwards from the longitudinal axis 22 in the upward direction, but as explained below, is not necessarily always the case. The floating structure may be provided with a moonpool 18 extending through the main section 14 and the upper section 12.

In figure 8 the main section 14 and the upper section 12 is shown having a cross section normal to the floating unit's 10 longitudinal axis 22 which has a regular octagonal shape with side faces 20. The shape of the cross section may, however, also be circular or of a regular polygonal shape other than octagonal. The advantage of using a polygonal shape is that flat plates rather than curved plates can be used during manufacturing of the centre barrel 1 1 of the floating unit 10 which is easier and cheaper than using curved plates. In addition, the corners 21 created where two side faces 20 are joined contribute to the damping of the floating unit.

By providing the floating unit with the upper conical section 12 which penetrates the still water surface 30, i.e. the conically shaped upper section 12 extends above and below the water surface, the pitch/roll motions and the heave motions of the single barrel floating unit may be decoupled. The flare angle φ that the outward facing sides 13 of the conical upper section 12 makes with the longitudinal axis (i.e. generally with a vertical line) is shown in Figures 7 and 9. The size of the flare angle φ depends on the main particulars of the floating unit 10 as will be explained below.

Referring to Figure 9, the distance from the waterline 25 down to the cylindrical part is "h". The conical upper section 12 will also extend a distance above the waterline, preferably at least a distance "h".

It is possible to develop an expression for a metacentric parameter KM taking into account the flare of the conical upper section 12. The main contribution from the flare is that it increases the waterline moment of inertia, but it will also affect the displacement and the vertical position of the centre of buoyancy.

By treating the flare as a section of a cone, both the KB and the BM values can be calculated. In general one may define the KM as a function of the following parameters:

where D is the equivalent diameter of the unit as explained above, i.e. if the cross section of the floating unit is polygonal ly shaped (for instance as an octagon), the diameter is selected such that π/4*Γ) 2 gives the same cross sectional area as the polygon of the actual floating unit under consideration.

T is the static ( still water) draught, φ is the flare angle that has to be found, x represents the vertical motion from the initial draught as a result of the motions of the floating unit.

The derivative of the expression for KM may now be found: δΚΜ(Ο,Τ,φ,χ) = dKM(D,T,cp,x)/dx

The resulting function may be plotted as shown in Figure 5 where the variation of the KM-value δΚΜ(Ο,Τ,φ,χ) is plotted for four flare angles and as a function of the draught T. Again, as an example D = 90 m in all four cases. As can be seen in Figure 5, it will normally be possible to find a value of the flare angle φ that will result in δΚΜ(ϋ,Τ,φ,χ) = 0 for any combination of diameter D and draught T.

The optimal flare angle may be found for any desired draught, but in the example below a value x = 0 is chosen, i.e. the still water draught, as this is considered the most correct draught. It would be possible to solve the equation δΚΜ(Ι),Τ.φ,χ) = 0 for many different values of the draught and a corresponding number of varying flare angles would be obtained. The result would be that the upper portion 12 of the floating unit would no longer be conically shaped, but rather have a curved shape similar to an upside down champagne bottle. This approach would theoretically be the most correct shape of the upper section 12, but since the upper section 12 in this case would have a double-curved shape, the upper section would be both difficult and expensive to manufacture. Therefore, for practical purposes, a constant value for the draught may be chosen, for example x = 0, whereby a conically shaped upper section 12 is the result having a flare angle corresponding to the chosen value of the draught.

Solving the equation δΚΜ(ϋ,Τ,φ,Ο) = 0 with respect to the flare angle φ, i.e. the value of x is set to zero, gives the flare angle that will assure no variation of KM (and thus GM). Consequently the parametric connection between heave motions and pitch/roll motions is decoupled.

In Figure 6 the result of solving the equation δΚΜ(Ο,Τ,φ,Ο) = 0 for a diameter of 90m is shown. As can be seen in Figure 6, for a draught T = 20m, a flare angle φ ~ 23° should be chosen to assure decoupling of heave and pitch/roll motions. It should be understood that values slightly above or below the flare angle for a given diameter and draught will also work, if not as well as the optimal value. In the example above, the most optimal value for the flare angle would be about 23°, but flare angles in the range of about ±20% of the most optimal flare angle can be considered usable, i.e. in this example the flare angle should at least fall within the range of about 18°-28°. It may also be noted that in the example above, for draughts larger than

approximately 32-33m (when the diameter is 90m), the flare angle is negative. This means that the conical upper section 12 should be inclined towards the longitudinal axis, i.e. with a gradually decreasing diameter in the upward direction of the longitudinal axis, in order to assure decoupling of heave motions and pitch/roll motions.

As explained, the tendency to get Mathieu motions depends on the D/T ratio, but it is possible to define a flare angle in the waterline area that will result in no variation of the GM stiffness and consequently no driving forces for parametric coupling between heave and pitch/roll for any combination of D and T.

The flare angle necessary to obtain this is defined by the mathematical equation given above which is also given in more detail in the appendix below.

Appendix

Below an example of the computation of the flare angle is given.

:= T + x η ·= 9Γ)

Define as initial case diameter = 90m, draught T = 30 m, flare angle = 20 dag. ψ := 20.A ¾

i, != 5 h is the distance between the parallell part and the operating waterline. + 2-tan(ip).(h + x) New diameter when unit is displaced x m from operating draft

Hzl (D,h,<p) :=

2-tan(ip) Height of the two cones defining the cone segment (assistance quantities)

Hz2(D,h,ip, x) := Hzl(D,h, w) + (h + x)

VolfD. T. Volume as funnction of geometry and motion amp.(x) from static waterline

Vertcal center of buoyancy (KB or VCB):

Moment of inertia of displaced waterline

I(D,h,<p,x)

BM(D,T,h,ip,x) : Metacentric height (BM)

KM(D,T,h,<p,x) := vcB(D,T,h,ip,x) + BM(D,T,h,9,x) Total metacentric heigh (KM)

Variation of KM as function of draft for various flare angles:

δΚΜ(ϋ,τ,ΐι,φ,χ) := !LKM(D,T,1I φ,χ) Derivating the KM function to find the variation as function of x

dx

T := 20, 21..40 Starting a loop for draughts from 20 to 40 m in step of 1 m φ = 20-deg Plotting the function for several flare angles to show that it is possible to fande a flare angle that passes through 0 The plot is made for diameter D = 90

ip3 := 10-deg φ4 := 1-deg

T

The fig shows the dirivative of KM as function of draught for several flare angles.

i := 0.. 30

Start loop for draughts from 15 to 45 m in step of 1 m

T c := 15 + i

Find flare angle that gives no Mathieu for various drafts:

j := 0..4

Start loop for diameters from 50 m to 130 m in step of 20 m

DD. := 50 + 20-j

^ . := root^KM^DD. ,TTR.,h,9,0) ,φ) Solve equation to find angle that gives the derivative of KM

Plot of optimum flare angle as function of draft, plotted for diameters from 50 to 130m in step of 20 m.