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List of Editors

Celso Pupo PesceUniversidade de São Paulo, Brazil (Chief-Editor)[email protected]

Marcelo de Almeida Santos NevesUniversidade Federal do Rio de Janeiro, Brazil (Chief-Editor)[email protected]

Michael M. BernitsasUniversity of Michigan, [email protected]

Belmiro Mendes de Castro FilhoUniversidade de São Paulo, [email protected]

Günther ClaussTechnical University of Berlin, [email protected]

Paulo de Tarso Temístocles EsperançaUniversidade Federal do Rio de Janeiro, [email protected]

Segen Farid EstefenUniversidade Federal do Rio de Janeiro, [email protected]

Odd FaltinsenNorwegian University of Science and Technology, [email protected]

Jeffrey M. Falzarano Texas A&M University, [email protected]

Antonio Carlos FernandesUniversidade Federal do Rio de Janeiro, [email protected]

José Alfredo Ferrari JrPetrobras, [email protected]

André Luiz C. FujarraUniversidade de São Paulo, [email protected]

Carlos Guedes SoaresUniversidade Técnica de Lisboa, [email protected]

Atilla IncecikUniversities of Glasgow & Strathclyde, UK [email protected]

Breno Pinheiro JacobUniversidade Federal do Rio de Janeiro, [email protected]

Jan Otto de KatA. P. Moeller-Maersk, Denmark [email protected]

Carlos Antonio Levi da ConceiçãoUniversidade Federal do Rio de Janeiro, [email protected]

Clóvis de Arruda MartinsUniversidade de São Paulo, [email protected]

Júlio Romano MeneghiniUniversidade de São Paulo, [email protected]

Torgeir MoanNorwegian University of Science and Technology, [email protected]

Helio Mitio MorishitaUniversidade de São Paulo, [email protected]

Celso Kazuyuki MorookaUniversidade de Campinas, [email protected]

Kazuo NishimotoUniversidade de São Paulo, [email protected]

Apostolos PapanikolaouNational Technical University of Athens, [email protected]

Floriano Carlos Martins Pires JrUniversidade Federal do Rio de Janeiro, [email protected]

Claudio RuggieriUniversidade de São Paulo, [email protected]

Claudio Mueller Prado SampaioUniversidade de São Paulo, [email protected]

Alexandre Nicolaos SimosUniversidade de São Paulo, [email protected] Sergio Hamilton SphaierUniversidade Federal do Rio de Janeiro, [email protected]

Célio TaniguchiUniversidade de São Paulo, [email protected]

Eduardo A. TannuriUniversidade de São Paulo, [email protected]

Pandeli TemarelUniversity of [email protected]

Armin Walter TroeschUniversity of Michigan, [email protected]

José Márcio do Amaral VasconcellosUniversidade Federal do Rio de Janeiro, [email protected]

Dracos VassalosUniversity of Strathclyde, United [email protected]

Murilo Augusto VazUniversidade Federal do Rio de Janeiro, [email protected]

Ronald W. YeungUniversity of California at Berkeley, [email protected]

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Marine Systems & Ocean TechnologyJournal of SOBENA

www.sobena.org.br/msot

Chief-Editors

Marcelo de Almeida Santos NevesUniversidade Federal do Rio de Janeiro

Celso Pupo PesceUniversidade de São Paulo

journal of

SoBEnaSociedade Brasileira de Engenharia naval

Volume 8 Number 1 June 2013

Marine Systems & Ocean Technology

Aims and Scope

The design process of marine systems is one of formulation, evaluation and modification. Very often the problems confronting the designer are effectively complex problems, particularly on the technical side. Analytical models have to be invoked and applied together with numerical and experimental simulations, guided by intelligent experience, at all levels of the design chain.

In the past these difficulties have been more concentrated on few particular types of marine vehicles and systems. In particular, naval architects have designed surface ships. Specialised methodologies and rules have been developed and accumulated in this field. Some excellent periodicals are dedicated to the coverage of researches and developments in this sector.

More recent technological developments, particularly in the offshore industry, have challenged this knowledge, introducing many, and often radically distinct departures from the more conventional designs. Hence, largely multidisciplinary technologies are pre-sently at the frontline, demanding fresh contributions not only from the naval architecture and ocean engineering fields, but also from all contributing areas as civil, mechanical, electrical, material, petroleum, coastal and oceanographic engineering, applied oceanography and meteorology and applied mathematics.

Marine Systems & Ocean Technology intends to contribute to this wide and rich technological scenario by providing a forum for the discussion of mathematical, scientific and technological topics related to:

• hydrodynamic and structural analysis of any fixed and floating marine systems (including ships and advanced marine vehicles),

• underwater technology (including submarines, robotics, design and operation of diving systems, surveys and maintenance systems, umbilical cables, pipelines and risers),

• computational methods in naval architecture, offshore/ocean engineering, coastal engineering and related areas,

• environmental studies associated with oil spills and leakage prevention and control, safety concepts and risk analysis applied to marine systems, wave-energy extracting devices and sea resources in general,

• ocean and river transportation economics, marine engineering and environmental protection, offshore support bases, offshore logistics.

Marine Systems & Ocean Technology is an editorial initiative jointly coordinated by SOBENA and CEENO. SOBENA is an abre-viation for Sociedade Brasileira de Engenharia Naval, a learned society founded in 1962 for promoting technological development. CEENO is a Scientific Network on Naval Architecture and Ocean Engineering organized in 1999 by leading members of the Brazilian scientific community afiliated to two universities and two research centers: COPPE/UFRJ, USP, IPT, CENPES.

Marine Systems & Ocean Technology (ISSN 1679-396X) is published twice a year and is owned by Sociedade Brasileira de Engenharia Naval - SOBENA, and is distributed freely to members. Rate for 2011 is R$ 200.00 for institutions and R$ 100.00 for individuals. Issues are airmail shipped. All subscriptions are payable in advance and entered on an annual basis.

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Abstract

With sea transport of heavy objects in focus, model tests of a barge in irregular waves have been performed. Securing the transported object to the deck of the barge is of vital importance, and an optimum load level to be used in the structural design is desirable. The aim is to investigate methods for predictions of barge roll motion and related sea fastening forces. Response from linear and non-linear numerical analyses is compared with results of model tests. It is found that the numerical analyses give slightly conservative results, and that the non-linear time-domain analyses gives only marginally more accurate results than the linear frequency domain method.

Keywords

Motion analysis; Transport barge; Model test; Forced roll; Free decay test; Irregular waves.

Fig. 1 Barge with transported object, global axes shown.

Vol. 8 No. 1 pp. 05-19 June 2013 Marine Systems & Ocean Technology 5

Rolling of a transport barge in irregular seas, a comparison of motion analyses and model tests

Asle Natskår1 and Sverre Steen2

1) Centre for Ships and Ocean Structures (CeSOS), Norwegian University of Science and Technology, Trondheim, Norway, Email: [email protected]

2) Department of Marine Technology, Norwegian University of Science and Technology, Trondheim, Norway

Submitted to MS&OT on January 16 2013. Revised version submitted on April 01 2013. Accepted on April 06 2013. Editor: Marcelo A. S. Neves.

6 Marine Systems & Ocean Technology Vol. 8 No. 1 pp. 05-19 June 2013

Nomenclature ay Acceleration in cog of transported object in sway direction, including the effect of gravity B Breadth (beam) of the barge B1 Linear damping (unit: Nms) B44,2 Quadratic roll damping (unit: Nms2) Beq Equivalent damping

Bm Breadth (width) of the transported object

Ce Drag coefficient for barge roll

cog centre of gravity

Cov Coefficient of variation, also called VX ,

VX= σX / μX

D Draught of barge

Db Diameter of bilge (2rb )

E[X] Expected value (mean) of variable X

g Accereration of gravity, g=9.81m/s2

H0 Half width over draught (=B/(2D))

h2 is the distance from the water line to the cog of the transported object

KC=UT/Db is the Keulegan-Carpenter number

KG Distance from keel to cog

m Mass of transported object M Mass of barge and transported object

M4(t) Roll moment

OG Distance from water line to cog, positive downwards (= D _ KG)

rb Radius of bilge

S Response, Extreme values

T Wave period

μX Mean value, E[X]. For discrete variable:

η Barge motion vector measured at still water level, η = [η1 η2 η3 η4 η5 η6 ]

T, index 1-6 means surge, sway, heave, roll, pitch and yaw, respectively.

θ0 Roll amplitude of barge

θ Barge roll angle (≡ η4)

ν Kinematic viscosity (ν=10-6m2/s)

Damping ratio. , where C is the spring (restoring) stifffness, M is the mass or rotational inertia and ω0 is the natural frequency in rad/s.

Variance. For discrete variable:

σX Standard deviation.

1 Introduction

In this paper we consider transport of large and heavy objects on a towed ocean going barge, as shown in Figure 1. Model tests of a Standard North Sea barge in scale 1:50 loaded with a module with a mass equal to 3500 tonnes in full scale have been performed. The transported object is secured to the deck of the barge by sea fastening. The load level for which the structural design of sea fastening is performed will impact largely on the amount of steel required for sea fastening and influence the time spent in port and the amount of labour required. Hence, an optimum load level to be used in the structural design is desirable. Several irregular sea states with large wave height have been run in the model tank, see Fig. 2. The aim is to investigate methods for predictions of barge roll motion and related sea fastening forces with regard to planning, design and fabrication of the sea fastening.

In practical engineering, linear calculations using potential theory are normally used for calculating forces in the sea fastening for given (predefined) sea states. More advanced methods do exist, e.g. the computer program Wasim from DNV (2011), but due to limited time and resources, the simpler linear methods are normally preferred.

For long transports where there is no possibility to seek shelter in case of adverse weather, the tow must be able to resist the environmental loads that, within a defined probability, may occur during the voyage. The environmental loads will then be based on extreme value statistics for the geographic area, the time of the year and the duration of the voyage. In order for the failure probability to be sufficiently low, the structural capacity of the barge, the transported object and the sea fastening need to be verified for a rather high design load. Based on environmental statistics, significant wave height, wave periods and design wind speed are found. Since the motions of the barge are normally found by linear motion response analyses using potential theory, it is of interest to see how good a linear analysis may be for the purpose. For practical cases, the motions may also be estimated by simplified criteria from design rules (DNV (1996/2000)) or standards (ISO (2009)), but that is not considered further herein. For design of sea fastening, the governing wave load direction is often beam seas, since roll motion of the barge will introduce the largest forces in the sea fastening system. The towed barge will under intact conditions not be exposed to severe beam seas, since the tug will seek to head up against the waves in adverse weather. However, in case of a tug engine failure or tow line breakage, the barge will drift and will typically be exposed to beam sea waves. Previously, the barge motions have been investigated for regular waves by Natskår and Moan (2010). It was then shown that the roll angles could be well described by linear analysis, as long as the additional damping from viscous effects was appropriately included. This matter is now further investigated for irregular waves. In this paper, viscous roll damping from free decay and forced roll model tests are measured. The measured roll damping is used as input to motion analyses of the barge in time and frequency domain. The results are compared with model tests of the barge in irregular waves.

Rolling of a transport barge in irregular seas, a comparison of motion analyses and model testsAsle Natskår and Sverre Steen


Table 1 Key figures for the barge, model scale numbers in parentheses.

2 Model tests

2.1 Barge model and test facilities

The barge tested is a standard North Sea barge with a raked bow and stern, as shown in Fig. 1. This class of barge is commonly used for transports of heavy objects. Key figures are given in Table 1. Several types of tests have been performed by use of this model. Forced roll tests and regular wave tests (Natskår and Moan (2010)), and also free decay roll tests were performed in Tank 1, see Tab. 2. Irregular wave tests were performed in Tank 2.

Fig. 2 Barge model in irregular waves.

A model of the barge in scale 1:50 is used. The model is made from divinycell foam with a density of 60kg/m3, reinforced with plywood plates in strategic areas. The model is covered with glass-fibre reinforced polyester and painted to achieve a smooth surface. The model is ballasted to a correct mass and cog by steel plates fixed to the transported object and in ballast rooms in the barge. The model may be fitted with either a bilge radius or a sharp corner, see Figure 3. The model has a slot 11 by 11 mm at the bilge. Rails with radius 11 mm or sharp corner may be fitted, enabling the same model to be used for test of full scale radius of 0.55 m and a sharp corner.

Froude scaling is used. The geometry of the model and wave elevations are then scaled by λ, time and velocity are scaled by , where λ=50. Accelerations and roll angles are the same in model scale and full scale. Linear roll damping, B44,1 is scaled by λ4.5, and quadratic roll damping, B44,2 , is scaled by λ5.

The model is moored by soft springs to prevent drift. The natural sway period is about one minute in full scale, hence the mooring lines are considered negligible for the motion of the barge in waves.

Fig. 3 Barge cross section, showing replaceable bilges. Cog1 is for barge and transported object, cog2 is for transported object only. Dimensions in mm.


Table 2 Key figures for the model test facilities used for the model tests. Tank 1 is the MC-lab, tank 2 is the extension of the Towing tank at Marintek in Trondheim, Norway.

2.2 Forced roll tests

Forced roll tests are performed in order to find the roll damping in calm sea. The barge model was set in a rig such that the barge rolled about the still water line, ref. Figure 4. Harmonic roll motions were applied, and the force required to perform the roll motion was measured. The equivalent roll damping found from these tests is shown in Figure 8.

Fig. 4 Barge model (without transported object) in rig for forced roll tests. Applied force and position were measured.

2.3 Free decay tests

Free decay tests are also used to estimate the viscous roll damping. The model is given an initial list (static roll angle), and is then suddenly released. The roll motion during the free decay is monitored. The results for the case with bilge radius in Figure 9 are based on eight decay tests. The sharp corner case shown in Figure 10 is based on ten decay tests.

2.4 Tests in irregular waves

The model has been tested in regular waves and irregular waves. Regular waves are documented by Natskår and Moan (2010). The irregular wave conditions are shown in Table 3. From each test except run 1201, a 1800 s long stationary time period is extracted, corresponding to about 3.5 hours in full scale. From

run 1201, which is the continuation of run 1200, a stationary period of 800 s is extracted.

Table 3: Significant wave height Hs (m), peak period Tp (s) and zero crossing period Tz (s), full and model scale values, for irregular sea states.

The wave spectrum applied in the wave tank is a Pierson-Moskowitz spectrum (see e.g. DNV (2007)). However, as the waves propagate along the tank, the spectra estimated based on measured wave elevations are slightly different from the applied spectra, a fraction of the energy in the measured spectra is shifted towards lower frequencies. For a Pierson-Moskowitz spectrum, the ratio between peak and zero crossing periods is Tp /Tz ≈ 1.4, while for the measured spectra the ratio is between 1.1 and 1.4, see Table 3.

2.5 Scale effects

The model of the barge is in scale 1:50. Froude scaling has been used, which implies that gravitational forces (wave load and wave radiation damping) and inertia forces (barge accelerations and added mass) are correctly scaled from the model to full scale. For the viscous damping caused by vortex shedding, the situation is different. The magnitude of the damping depends on the type of flow, analog to the drag load on a cylinder. The load occurs when there is separation of the flow at the submerged corner of the barge. For a sharp corner there is always flow separation. For the case with rounded corner, flow separation with vortex shedding occurs when the Keulegan-Carpenter number, KC = UT/Db, is larger than about 2 (Faltinsen (1990)), where U is flow amplitude, T is flow period and Db is characteristic length of the body, taken as bilge diameter in our case. If we assume 10º roll amplitude with a full scale period of T=8s (U ≈ ωθ0 B/2, Db=2rb ) KC = 15 in both model scale and full scale. There will then be separation with vortex shedding in both model scale and full scale for the barge with rounded corner. The Reynolds number is however scale dependent, and will be different in model scale and full scale. Reynolds number, Rn=UDb ./ν (Faltinsen (1990)) is equal to 6 . 103 and 2 . 106 in model scale and full scale, respectively. In model scale, the flow is in the subcritical regime, and the boundary layer at the bilge is laminar. In full scale, the flow is in the transcritical regime, and the boundary layer upstream of the separation point is turbulent (see e.g. Faltinsen (1990)). For the case with sharp corner, there should not be any significant scale effects, since there will be vortices starting from the corner of the barge cross section in both scales. Since there will also be vortices shed for the barge



with rounded corner, and the bilge radius is relatively small, it is concluded that the pressure distribution will be quite similar in both model scale and full scale, and hence no scale effect is accounted for.

Another effect could also justify neglecting scale effects. As is seen from Figure 5, the effect of the flow regime on the drag coefficient is large for a smooth surface, and less accentuated for a rough surface. The barge model has a smooth surface (and the roughness is not so important in the subcritical regime). A full scale barge is likely to, due to paintwork, marine fouling and welding seams, have a rough surface (Newman (1977)). Considering rolling, this will have a positive effect, since it may result in a larger drag coefficient than for a smooth surface in the transcritical regime. (With regard to towing, the effect is negative as it lead to increased towing resistance, however that is not a concern here.)

Fig. 5 Drag coefficient as a function of Reynolds number for a cylinder (from Achenbach (1971), Fig. 7).

3 Numerical methodology

3.1 Equation of motion for barge

The equation of motion for the barge is expressed as

(1)

where l ω is the angular frequency of the wave in rad/s

l F0(ω) is the complex wave load amplitude, given as the wave elevation amplitude multipied by the transfer function,

l M is the mass matrix of the barge including the transported object

l A(ω) is the hydrodynamic added mass matrix

l B1(ω) is the linear damping matrix from potential damping (wave radiation)

l B2 is the quadratic damping matrix and represents the viscous damping (vortex shedding) at the bilges. In our case, this matrix only has one non-zero element; the diagonal term for roll, B2,44

l C is the restoring matrix l η = [η1 η2 η3 η4 η5 η6 ]

T, where index 1-6 means surge, sway, heave, roll, pitch and yaw, respectively

l the dots mean time derivatives.

The wave load, F0(ω), the added mass, A(ω), and the potential damping matrix, B1(ω) are calculated by the sink-source method (based on potential theory) and is a function of the wave frequency, see e.g. Faltinsen (1990). In analyses for practical engineering purposes, the wave power spectrum to be used in the response analyses will be a design spectrum, e.g. Pierson-Moskowitz (DNV (2007)). However, in the analyses within this paper, to be compared with results from the model tests, wave spectra are calculated from wave elevations measured in the model tank during wave calibration. The Matlab toolbox Wafo (2011) is used for estimating power spectra.

The viscous part of the damping is not calculated by the sink-source method and is hence the challenging part. In Eq. (1) it is represented by a quadratic term, B2(ω). However, a cubic term could also be included. This non-linear term makes the equation more cumbersome to solve than a linear equation. Therefore, the damping term is often replaced by an equivalent damping term, and then the equation may be solved in the frequency domain. Alternatively, the equation may be solved in time domain, and then the non-linear damping is included directly.

The coordinate system used in frequency domain analysis is earth fixed, while in time domain analysis, a ship fixed coordinate system is used. For small motions, the choice of coordinate system is not important. For large motions, the choice of coordinate system will affect the results, ref. Sec. 3.4.

In the model tests with irregular waves, some of the largest waves in the time series tend to flow over the barge deck. This happens mainly for the sea states with shortest period. From observation of the model tests, slamming does not occur, the water rather flows over the deck. The effect on the barge motion is assumed to be small and it is not included in the numerical analyses.

3.2 Solving the equation in frequency domain

In order to solve the equation in frequency domain, the quadratic damping term is linearized. For regular waves, the



equivalent linear damping is found by demanding that the same amount of energy should be dissipated from the linear system as from the non-linear system. The equivalent damping is then

(2)

where θ0 is the roll amplitude. For an irregular sea state, equivalent stochastic linearization leads to (Price and Bishop (1974))

(3)

By assuming has a normal distribution (and since the mean value is zero), we get

(4)

and the equivalent damping is then

(5)

When the damping has been linearized and the motion is expressed as η = η0exp(iωt), the equation of motion can be written as:

(6)

where Beq(ω) is B1(ω) with the value for B44,eq added into position (4,4).

3.3 Solving the equation in time domain

An alternative to solving the equation of motion in the frequency domain by equivalent linearization of the damping as discussed, is to solve the equation of motion in time domain. This method is based on work by Cummins (1962) and Ogilvie (1964). A short description of the method can be found in Marintek (2009). In time domain, the equation of motion is expressed as:

(7)

where l f(t) is a realisation of the wave load l A∞ = lim A(ω)

ω→∞

l h(τ) is the retardation function matrix, it can be

calculated based on the added mass or damping.

In the present analysis, the retardation functions are calculated based on the frequency dependent damping:

(8)

h(τ) is a 6x6 matrix with non-zero elements on the diagonal and in position (1,5), (2,4), (5,1) and (4,2) for a symmetric barge (i.e. where B1(ω) has non-zero elements).

The time dependent load is calculated as:

(9)

where is the impulse response function and is the wave elevation. The impulse response function is calculated as:

(10)

where is the transfer functions for wave loads as calculated by potential theory.

The time series for the wave elevation are generated by adding harmonic components using Fast Fourier transform (FFT), see e.g. Marintek (2009). The length of the time series is then limited to Tmax = 2π/Δω where Δω = 2π/(NΔt). The maximum number of time steps is taken as N= 217, and the time step used is Δt = 0.02s. The maximum simulation length is then Tmax = NΔt = 2621s. A simulation length equal to 1800 s is used in the analyses.

3.4 The effect of body fixed coordinate system

The coordinate systems used in Equations (6) and (7) differ from each other in the sense that the first is solved in global (earth fixed) coordinates and the second is solved in local (ship fixed) coordinates. Using a body fixed coordinate system in the time domain analysis introduce some additional terms in the equations of motions. For small waves and small ship motions, these terms are negligible, but in severe seas they will affect the solution.

The equations of motions in a ship fixed coordinate system are derived using the same method as Faltinsen (2005)1. The velocity is written as: u = ui + vj + wk, where i, j and k are unit vectors in surge, sway and heave directions, and they are functions of time. The rotational velocity in roll, pitch and yaw are expressed as Ω = [p q r]T. The time derivative of the velocity is then:

(11)

We consider a barge in beam seas, and then u, q and r are equal to zero (since the barge is symmetric). The equations of motions can now be formulated based on Newton’s second law. The equation of motion in roll is formulated by setting the roll moment equal to the time derivative of the moment of momentum. The equations of motions in sway, heave and roll are then:

(12)

where Fy , Fz and Mx are the hydrodynamic forces acting on the ship (they include the restoring, damping and retardation term

1 However, the formulas are slightly different, since in Faltinsen (2005) section 10.9.1, the origin is in the centre of gravity (zcog = 0), the vertical axis points downwards and Φ is used for the roll angle, while we have zcog ≠ 0, vertical axis upwards and use Θ for roll angle.



from Eq. (7)). The terms wp, vp and p2 are of second order and are negligible for small motions. For large wave heights and hence large ship motions they contribute to the difference in results from the linear and non-linear analysis.

3.5 Forces in sea fastening

The forces in sea fastening were not measured during the model tests. The model was a rigid body. Displacements and accelerations were measured. For design of sea fastening, the forces based on motions and accelerations will be governing for the load. In addition, relative stiffness between barge, sea fastening and transported object will affect the load distribution. Sea fastening should normally be designed aiming for a simple load pattern, as required by e.g. the DNV-rules (DNV (1996/2000), Pt.1 Ch.4 Sec. 2.1.1.5). In the current work, a simple load pattern is assumed, and the vertical and horizontal loads are calculated based on dynamic equilibrium. In a ship fixed coordinate system, the horizontal (lateral) forces, and the vertical forces in points 1 and 2 are then (see Fig. 6)

(13)

(14)

where

l Bm = 0.4 m is the width of the transported object (i.e. the distance between the supports)

l m = mass of transported object

l Im = rotational moment of inertia for the transported object ( )

l ay = acceleration in cog of transported object in sway direction , including the effect of gravity ( gsinη4 )

l rg = 0.163m is the radius of gyration for the transported object

l h = 0.2m is the distance from bottom of transported object

to cog

l h2 = 0.3m is the distance from the water line to the cog of the transported object.

In Eq. (14), the first term is static load and the second term is due to heave acceleration. The third term is due to sway accelerations in module cog and roll motion, while the fourth term is due to roll acceleration. The fourth term is small compared to the second and third term. The second and third terms are of similar size. Since we use + for the third term when calculating FV1 (on windward side) and _ when calculating FV2 (on leeward side), and the phase difference between the second and third term is relatively small, FV1 will be larger than FV2. Hence, only FV1 is considered. In order to get an expression for the dynamic part of the load only, the static part is subtracted. The expression is also normalised by mg. The expression for the dynamic part of the governing load then becomes:

(15)

(16)

For linear analysis it is normally assumed that cosη4 _ 1 ≈ 0 and sinη4 ≈ η4.

Fig. 6 Transported object. Definition of horizontal and vertical forces (in ship fixed axes) from the sea fastening forces acting on the transported object. Accelerations ay and az act in cog of transported object. Wave direction is in positive y-direction.

By use of eq (15) and (16), the forces in the sea fastening may be calculated. In practical engineering, these forces will be input for structural design of sea fastening elements and also verification of structural capacity of the barge and the transported object. Within the present work, the forces are calculated based on results from model tests and numerical calculations, ref. Tables 8 to 11.

3.6 The effect of body fixed coordinate system

In the forced roll tests, the model was rolled about the water line (OG=0).

Fig. 7 Rotation axes (roll centres) for free decay tests (left), and forced roll tests with rotation about still water line.



In the forced roll tests, the damping is estimated from the applied roll motion, θ(t) = θ0cos(ωt) and the measured roll moment, M4(t). The dissipated energy is expressed as the work performed by the roll moment (∫ M4(t)dθ). The equivalent (total) damping is then expressed as (Natskår and Moan (2010)):

(17)

where l n is number of cycles the damping is averaged over

(n = 10 is used here)

l θ0 is the roll amplitude in the harmonic roll motion

l ω is the roll frequency.

For the free decay tests, we use the classic method by fitting a straight line through the points from the model tests, as described by Faltinsen (1990). There are also alternatives, e.g. the method proposed by Fernandes and Oliveira (2009), where a bi-linear curve is fitted to the results. However, a straight line is convenient in order to split the damping into a linear and a quadratic part. The damping is then estimated from the logarithmic decrement:

(18)

where θi-1 and θi+1 are two successive amplitudes with time period Td between them. Since the logarithmic decrement is related to the damping ratio as δ ≈ 2πξ (see e.g. Clough and Penzien (1993)), and since ξ = Beq /(2(M44+A44 )ω), the equivalent damping is calculated as:

(19)

From Eq. (2) it is seen that if the equivalent damping from Eq. (17) is plotted as a function of 8/(3π)ωθ0 , and a straight line is fitted through the results, then B1 and B2 can be read directly from the plot (Faltinsen (1990)), see Figure 8. The model tests are performed for the natural period of 1.2 s and the roll angles are, 5º, 10º, 15º, 20º and 25º, counted from left to right in Figure 8. It is seen that the points do not form a straight line, but a curve. In the chosen coordinate system in Figure 8, with roll velocity amplitude at the abscissa and equivalent damping as ordinate, quadratic damping is represented by a straight line, refer to Eq. (2). A curved line will correspond to higher order damping, e.g cubic damping, mathematically expressed as . Other work has also shown that cubic damping may give a good representation (Ewers et al. (1979), page 34). However, considering the viscous damping as a drag force makes quadratic damping the natural choice.

In Figure 9 and 10, equivalent damping calculated from Eq. (19) is plotted as a function of 8/(3π)ωθi for rounded and sharp corner, respectively. θi is the amplitude for cycle no. i (θis used in the figures).

In the free decay tests, the model rolled about a point close to the centre of gravity, located 0.17 m above the water line, OG = _0.17m. The measured results are given in Table 4.

Fig. 8 Equivalent roll damping from forced roll tests, at natural roll period, and straight lines fitted by linear regression.

Fig. 9 Roll damping from free decay tests and straight line fitted by linear regression, for barge with rounded corners.

Fig. 10 Roll damping from free decay tests and straight line fitted by linear regression, for barge with sharp corners.



Table 4 Quadratic roll damping from model tests.

It is seen that there is a relatively large scatter in the results from the free decay tests; the correlation coefficients are about 0.8 for the results in Figure 9 and 10. The 95% confidence interval for the quadratic damping for the bilge radius case extracted from Figure 9 is B2 = [6.3 _ 8.3]Nms2. The confidence interval for damping in the sharp corner case shown in Figure 10 is B2 = [7.1-10.6]Nms2.

The values for which the fitted lines in Figures 8 to 10 cross the vertical axis are interpreted as the linear part of the damping according to Eq. (2).

The linear non-dimensional roll damping is b44,1 = B44,1 from model tests for roll about the

water line, ref. Fig. 8. For roll about the centre of gravity, the non-dimensional damping values from model tests are 0.003 and 0.02 for rounded and sharp corner, respectively, ref. Fig. 9 and 10. This damping is compared to the wave radiation damping calculated from potential theory. Linear damping from potential theory is practically the same for a barge with sharp corner as with bilge radius. The damping varies with the frequency, but here we only consider the damping at the natural frequency. For roll about the water line, the non-dimensional linear damping is calculated to b44,1 = 0.04, i.e. the same as the damping from the model tests. For roll about cog, the potential damping is calculated to B44,1 = 0.006. This value deviates from the model tests results. However, there is a certain scatter in the test results, ref Fig. 9 and 10, and the potential damping is relatively low for roll about cog. That may be the reason for the difference between the theoretical and experimental values. However, since the damping is low in this case, the deviation is less important. The potential damping is practically zero for a roll centre at a height above barge bottom equal to half the barge width, i.e. 0.21 m above still water line. This means that according to potential theory, no waves will be radiated from the barge when it is rolled about this point. The water displaced by the roll motion will move back and forth around the bilge corner, and not radiate waves.

The numeric values of the quadratic roll damping as extracted from the model tests varies considerably between forced roll and free decay tests, ref. Table 4. The roll damping measured in free decay tests is larger than the results from forced roll tests. The reason for the variation in roll damping depending on test method is due to different location of roll centre and variations in drag coefficient. These effects are further seen in the following section.

3.7 Theoretical estimate of non-linear roll damping

In the present analysis, a method based on Tanaka (1961)

is used. This method is also shown by Chakrabarti (2001). The force from the viscous damping is written on the form of quadratic drag force. The total force may be expressed as

(20)

(ref. Tanaka (1961) Eq.1 and Chakrabarti (2001) Eq. 13). Awet=(B+2D)L is the wet area of the barge and the length of the barge is set equal to the equivalent length, L=M/(ρDB) = 1.59 m in model scale. Cd is a drag coefficient. The force acts on the submerged part of the barge. However, since the force is mainly due to vortex shedding, it is assumed to act as a concentrated force at the barge bilges, Fdrag / 2 at each side, ref. Fig. 11. F0 is the component of Fdrag contributing to moment about the point 0 (i.e. F0 is perpendicular to the line from the bilge to 0). The moment about 0 is now M=2F0r0. With reference to Fig. 11 we see that (v is the angle between F0 and Fdrag ). The roll moment about point 0 is given as:

(21)

The damping is then expressed as:

(22)

Set

where OG = D _ KG. The origin in the axis system (point 0) is located z0 above the still water line, and we set .

Fig. 11 Barge cross section and definition of drag forces in simplified vortex shedding model.

By this method, the moment is calculated about this origin, while the barge rolls about the cog. Introducing H0=B/(2D), the damping is expressed as:

(23)

The drag coefficients are found by setting the expression in Eq. (23) equal to the damping from Table 4. For roll about cog (z0

= _OG = 0.17m), the drag coefficient is Cd=0.35 in the sharp



corner case and Cd=0.30 in the bilge radius case. For roll about water line (z0 = OG = 0), the drag coefficient is Cd = 0.17 in the sharp corner case and Cd = 0.13 in the bilge radius case.

Tanaka (1961) showed that the drag coefficient in Eq. (20) varies with the position of the roll centre. He presented the drag coefficient for B/KG ratios up to 4. This drag coefficient is shown with solid line in Fig. 12 (actually, the numbers are taken from Chakrabarti (2001), where the drag coefficients from Tanaka (1961) are given in tabular form). In the same figure the drag coefficients found from fitting Eq. (23) to the model tests for the barge with sharp corner is shown. The model tests results exist for B/KG ratios equal to 2.4 and 9.2, and they represent an extension of the range from Tanaka. A straight broken line is drawn between the results, to illustrate the trend. Equation (23) is convenient to use in cases where the reference system does not coincide with the centre of gravity (since the same model then can easily be used for varying cog).

Fig. 12 Drag coefficient in Eq. (20) as a function of roll centre height.

Ikeda (1993) used the following formula Eq. (24) for equivalent roll damping of a barge with a sharp corner and limited to about 5º roll angles:

(24)

(This method is also described by Chakrabarti (2001).) Equation (24) is based on free decay and forced roll model tests.

In Eq. (24), the equivalent damping is given. In order to convert to quadratic damping, Eq. (2) is used, giving B44,2 = 3πB44,eq /(8θ0ω). The quadratic roll damping for a barge with sharp corner is then

(25)

This formula can be used to calculate the roll damping moment about the roll axis, which is assumed to be in

the centre of gravity.

3.8 Barge roll damping numerical values

For free barge motion in irregular waves, the barge is assumed to roll about an axis close to the cog, so OG = _ 0.17m is used, even if a clearly defined roll centre does not exist (Faltinsen (2005) section 7.2). The origin in the axis system used in the numerical analysis is in the water line, hence z0 = 0 when calculating the roll damping from Eq. (23). The quadratic roll damping is then B44,2 ≈ 6Nms2 for the barge with bilge radius (Cd = 0.3), equivalent to B44,2 =1.8 ⋅ 109Nms2 in full scale.

3.9 Extraction of extreme values

Within this paper, the barge motions are calculated using one linear and one non-linear method. The results from the linear method are in the frequency domain, while the results from the non-linear analysis and the model tests are in the form of time series with barge motions, wave elevations etc. A method for estimating extreme values must be chosen. Several methods for estimation of extreme value are available.

For linear (frequency domain) analysis, a common method is to assume Rayleigh distributed maxima.2 The expected extreme value is then calculated from the well known formula (see e.g. Clough and Penzien (1993)):

(26)

where σX is the standard deviation of the response, n is the number of cycles during the time period considered and γ = 0.5772. The extreme values are calculated for a three hour storm period (T = 1527s in model scale), the number of cycles is then n = T/Tz , where Tz is the zero upcrossing period for the actual response.

For time series from non-linear analyses, the maxima may be assumed to follow a Weibull distribution, and based on that, the extreme values are estimated. Extreme values can also be extracted by the Acer method. Gaidai et al. (2010) compare results from the Acer method with the Weibull method, indicating that the Weibull method give somewhat larger values than does the Acer method.

The Weibull fitting method is described by Nascimento et al. (2011), comparing the Hermite polynomials method by Winterstein (1988) with several methods based on the Weibull fitting approach using two and three parameter Weibull distributions fitted to the tail of the distribution from time series. They investigated fitting the distribution to different fractions of the data set, from 10% to 40% of the largest maxima.

In this paper, we choose to use the Weibull fitting approach, because it is an engineering friendly method and is analogue to the Rayleigh fitting approach for the linear case. The Weibull distribution is fitted to the 30% largest maxima (one maximum for each zero-up-crossing).

A two-parameter Weibull distribution is described as:

2 The Rayleigh distribution is a special case of the Weibull distribution, see Eq. (27), with a = √2 σX and b = 2. Equation (26) then follows from Eq. (29) to (31).



(27) When the local maxima follow a Weibull distribution, the extreme values can be described by the Gumbel Type I extreme value distribution:

(28)

The parameters in the Gumbel distribution are found as (see e.g. DNV (2007), section 3.5.11.6)

(29)

(30)

where a and b are the parameters in the Weibull distribution, and n is the number of cycles. The extreme values are calculated for a three hour storm period. From the estimated Gumbel parameters, the expected extreme value Smax is calculated as (see e.g. Hahn and Shapiro (1967, reprinted 1994), page 113):

(31)

The computer program Simo (Marintek (2004)) is used to solve the dynamic equation, Eq. (7). The results are time series for each of the responses. Similar for the model tests, we have time series for each of the responses. The simulation length in the dynamic analysis is about 2100s, then a part in each end is removed and 1800s (same as in model tests) is used to extract statistics (a and b). The extreme values (i.e. α, β and Smax ) are calculated for a period of three hours in full scale (1527s in model scale).

3.10 Precision error estimate

In order to estimate the precision error for the model tests, results from a series of seven runs of the same regular wave are statistically analysed. The wave period was 1.2 s i.e. the roll natural period. The wave height was 0.22 m, i.e. the wave steepness is 1/10. Heave, roll and sway motions, and also sway accelerations and sea fastening forces are analysed. It is seen from Table 5 that the uncertainty in a single measurement is about 5%, and the coefficient of variation, Cov, is about 2%.

Table 5 Presicion error estimate for heave, roll and sway motion. Wave amplitude 112 mm, T = 1.2 s. S = 1/10. 7 repetitions.

4 Comparison between model tests and calculated results

Results from numerical analyses are compared with model tests results. Both extreme value statistics based on three hour storm duration (1527 s in model scale) and standard deviations of the response are compared. The deviation between the calculations and the model tests is defined as the ratio between the response from the test and the numerical result:

where (32)

S is the response. Index Test means that the response is from the model tests. Si is equal to Slin and Snl for the linear and nonlinear responses, respectively. The selected responses are roll angle and vertical and horizontal forces in the sea fastening, calculated from Eq. (15) and (16), i.e. S = θ, FV1,dyn /(mg) and FH /(mg). The results for XS are shown in Table 6 to 11 for the wave conditions from Table 3. The average value of XS is the bias, see e.g. Naess and Moan (2005), section 5.8.4.2.

Table 6 Roll angle, S = θ, degrees, compare standard deviations.

Table 7 Roll angle, S = θ, degrees, compare maximum values.



Table 8 Vertical force, , compare standard deviations.

Table 9 Vertical force, , compare maximum values.

Table 10 Horizontal force, , compare standard deviations.

Table 11 Horizontal force, , compare maximum values.

5 Discussion of results

The viscous damping measured in the model tests were for a barge in still water. For a barge in waves, the relative velocities between barge and water particles will be affected by the incoming waves. Standing (1991) investigated this effect by calculating the roll response for a barge with and without the effect of the water particle motions from incoming waves. He analysed a barge with sharp corners in regular waves with height 3 m and in irregular waves with 9 m significant wave height. He found that the water particle motion had little effect on the barge roll motions. The reason was that the bilge velocity from barge rolling was larger than the water particle velocity (at least for moderate wave heights), and that the water particle velocity is not in phase with the bilge velocity. Based on this, the measured viscous damping is used directly without scaling to account for relative particle motion.

Considering results from the linear analysis, the standard deviations for roll motion and horizontal sea fastening force are almost equal to the model tests, and for vertical sea fastening forces the standard deviations are over estimated, with a bias of about 0.7. The linear analyses overestimate the results with respect to extreme values for roll angles and sea fastening forces in all the tested sea states. The bias ranges from 0.6 to 0.9. The non-linear analyses under estimate the standard deviation of the roll motion, with a bias of about 1.2. For sea fastening forces, the bias for the standard deviation



is practically 1.0. The extreme values for the roll motion are generally overestimated from the non-linear analyses, with an exception for two sea states. The bias ranges from 0.84 to 1.1. Extreme values for the sea fastening forces are overestimated from the non-linear analyses, with a bias of 0.63-0.86.

The ratio between the maximum values and the standard deviations in Tables 6-11 varies depending on the methods of analysis, and it also depends on the response in question. In the linear analysis, the ratio is slightly less than four, as expected. In the non-linear analyses, the ratio varies between 3.3 and 5.3, depending on the response. The ratio from the model test varies between 2.7 and 4.1. The ratio between the maximum roll angle and the standard deviation is 3.4-3.9 for the non-linear analysis, i.e. close to the results from a linear analysis with Rayleigh distributed maxima. The similar ratio from the model tests is between 2.7 and 3.2. The reason for this low ratio may be that the roll amplitude is limited upwards by physical effects not captured in the numerical analyses. For example, in the numerical analysis, a linear restoring stiffness is applied. Hence the bilge could exit the water and the effect would not be included in the analysis. In the model tests, a bilge water exit would correspond to a changed restoring stiffness. No exit of the barge bilge corner was observed in the model tests; the reason could be the non-linear restoring stiffness. Another effect may be non-linear wave making in the model tests related to interactions between the barge bilge and the free water surface, as vortices were seen on the free surface in the tests. These effects may be relevant in order to explain the relatively low ratio between the maximum roll angle and the standard deviation, however they are considered to be outside the scope of this paper. The ratios between the maximum values and the standard deviations will also vary based on the method chosen for calculating the maximum (extreme) values, as described in section 3.9.

When the viscous damping from Eq. (23) with Cd for roll about cog is used in numerical analysis of a freely floating barge in irregular waves, the numerical results are conservative, in the sense that the sea fastening forces calculated from the numerical analyses are larger than the forces found from the model tests, as seen in Tables 9 and 11. The sea fastening forces are one of the main deliveries from the barge motion analyses for sea transports of large objects, and will be input to structural design, hence greatly affecting the cost of the transport. From a safety point of view, overestimated forces are good, but from a commercial point of view, the forces should not be overestimated too much.

The time series from the model tests are long enough (1800s in model scale) to create a quite stable standard deviation. If we rerun the non-linear time domain analysis several times with different seeds, the 95% confidence interval for the standard deviation of the roll motion will be within ±6% of the average. The 95% confidence interval for the maximum values of the roll motion will be within ±11% of the average (based on 7 runs with different seeds of seastate no. 1205, Tab. 3). The confidence intervals for the forces FV1 and FH

are smaller than for the roll motion.

There is a deviation between the results from the linear (frequency domain) and non-linear (time domain) analyses. The standard deviation of the roll motion in Table 6 is the most basic result from the analysis and is initially expected to be almost similar in the two type of analyses, since the non-linear roll damping is relatively small. However, the linear analysis assumes small (infinitesimal) motions, and the equations of motion are formulated in an earth fixed coordinate system. In the non-linear analysis, the formulation is not limited to small motions, and the equations of motion are formulated in a ship fixed coordinate system. This formulation introduces some non-linear terms in the equations, as shown in Sec. 3.4. These non-linear terms are negligible for small ship motions, but not for large wave height and ship motions. It is seen in Table 6 that the deviation is largest for the most severe sea states (run 1205 and 1206). (If the time domain analysis is run with linear roll damping only, there is still a difference in the results between time and frequency domain analyses for large wave heights.) It is not obvious which one is the better method. Both methods are based on loads from potential theory, and they represent approximate solutions. Since the non-linear method includes the quadratic damping directly; linearization is not necessary and the damping is more accurately described. Hence, from a technical point of view, the non-linear method is preferred. However, since the non-linear analyses are run in time domain, it is more tedious to extract results than from the linear analysis run in frequency domain. The available computer software will decide whether non-linear analyses are feasible in practical engineering.

To see the sensitivity in the motion analyses with respect to roll damping, the analyses were rerun with the viscous roll damping increased and decreased with 15%, respectively. The results (Slin and Snl in Table 6-11) are decreased respectively increased with about 5-7%.

The quadratic roll damping resulting from viscous damping may for a barge with sharp corner be estimated from Ikeda’s formula, Eq. (25), when the origin of the axis system in the analysis coincides with the centre of gravity. It may also be based on results (drag coefficients) from Tanaka supplemented with the result from the current model tests, as described in Eq. (23), this formula also accounts for the axis origin not coinciding with the cog. The two formulas are compared in Fig. 13, where they are plotted on dimensionless form as a function of B/KG. (Origin of axis system assumed to be in the cog in Eq. (23), in order to compare with Eq. (25).) It is seen that the two formulas have similar pattern when plotted as a function of B/KG, but the values differ. For the larger B/KG ratios, Ikeda’s formula yield larger damping values than the results from the model tests presented within this paper. For barges with rounded bilges, the viscous damping will be smaller. From the model tests it is seen that the quadratic damping for the barge with bilges is 75% to 85% of the sharp corner (ref. Tab. 4). Hence, for practical engineering cases, the damping from Eq. (23) may be scaled accordingly.



Fig. 13. Quadratic damping as a function of the B/KG ratio based on drag coefficients from Tanaka and the model tests (Eq. (23)) and Ikeda (Eq. (25)).

6 Summary and Conclusions

The forces in the sea fastenings for beam sea conditions depend on the roll angle and the sway, heave and roll accelerations of the barge. The roll motion of the barge obtained from the numerical analyses depends on the roll damping applied in the analyses. If only wave radiation damping as calculated by potential theory is applied, the motion and forces in sea fastening will be highly overestimated. Additional viscous roll damping caused by vortex shedding, not included in potential theory, should be added. However, if a too large viscous roll damping is applied, the barge motions will be too heavily damped, and the design forces will be underestimated.

In order to predict realistic results for roll angles and barge accelerations, the roll damping to be used must be chosen with care. In the present work, viscous roll damping for the barge has been calculated considering the damping as a result of a drag force with drag coefficients taken from model tests. The damping has been applied in a linear frequency domain analysis and a non-linear time domain analyses of the barge in irregular waves. The barge roll motion and typical sea fastening forces are compared with model test results. There is a relatively good agreement between analyses and model tests. However, the degree of agreement varies with the response, e.g. the linear analysis shows a good agreement with the model tests for roll amplitudes and horizontal sea fastening forces, while for the vertical sea fastening forces the deviation is relatively large. There is not documented any clear benefit

from running the non-linear time domain analysis, as the predictions from the linear frequency domain analysis are of similar accuracy. In the cases tested, the numerical analyses over predict the response compared with the model tests, i.e. the predictions for extreme values are to the safe side with respect to structural failure.

7 Acknowledgements

The model tests and the first author’s work are financed by the Research Council of Norway (RCN) through the Centre for Ships and Ocean Structures (CeSOS) at the Norwegian University of Science and Technology (NTNU). The first author has also received financial support from DNV through Det Norske Veritas’ Education Fund. The support is highly appreciated. RCN and DNV had no active roles in the research work. The first author would like to thank Professor Torgeir Moan at CeSOS for highly valuable guidance and help throughout the work.

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AbstractExternal- and internal-ship (due to sloshing and water on deck) slamming phenomena as well as slamming on marine structures have been systematically and comprehensively described. Main scenarios were identified. Quantitative and qualitative influence of physical parameters on slamming was critically examined and the relevant factors identified. Theoretical, numerical and expe-rimental tools have been complementarily or alternatively used to carry on the analysis.

Keywords Slamming; whipping; wetdeck; hydroelasticity; green water; sloshing.

1 Introduction

Slamming is of concern for structural design of ships, offshore platforms, coastal structures and very large floating structures (VLFS). Marine operations involving lifting or lowering of objects through the free surface need knowledge about the water entry and exit loads occurring when the object is in the splash zone. Water entry and exit loads are associated with increasing and decreasing wetted surface, respectively. Slamming is normally connected with water entry. However, both water entry and exit loads matter for global wetdeck slamming effects. Slamming in membrane tanks used for LNG transportation is probably the most complicated slamming problem because several flow parameters involving different physical effects have to be considered. This fact limits the applicability of theoretical and numerical methods and causes difficulties in scaling model test results to full scale. Slamming is discussed in the books by Faltinsen (1990, 2005) and Faltinsen and Timokha (2009). The latter book deals exclusively with sloshing.

External slamming on ships causes both local and global structural response. The global effect is called whipping. The slamming analysis should ideally be simultaneously integrated in the global ship behaviour at least when the slamming effect occurs on the same time scale as the global wave-induced ship response. However, the state-of-the-art procedures for local slamming analysis consider slamming separately with given forcing of the relevant ship part. When it comes to global analysis, the hydrodynamic problem is in engineering analysis divided into sub-problems involving linear hydrodynamic loads, slamming loads and nonlinear Froude-Kriloff and restoring loads. A rational procedure solving the fully nonlinear hydrodynamic problem has still theoretical challenges and becomes impractical due to the required computational time when examining the stochastic behaviour in different sea states. Hydroelasticity is important for global loads, but matters also for local effects in the case of extremely high slamming pressures of very short duration when the pressure rise time is on the time scale of natural structural periods causing significant structural stresses. Very large pressures that are sensitive to inflow conditions may occur when the angle between the impacting free surface and the hull surface is small.

Slamming on ships and marine structures

Odd M. FaltinsenCeSOS, Department of Marine Technology, NTNU. Trondheim, Norway [email protected]

Presented initially by the author at the Ten-Years LabOceano Celebration Workshop, April 29-30, 2013, Rio de Janeiro, Brazil. MS&OT Editor: Sergio S. Sphaier.


It is common in a local slamming analysis to estimate the hydrodynamic loading by assuming a rigid structure and then to apply the loading in a quasi-steady manner when the resulting static structural elastic and plastic deformations and stresses are calculated. This means that hydroelasticity is not accounted for. The fluid flow is affected by many physical features, such as compressibility and air cushion. Because it is complicated to solve the complete hydrodynamic problem, approximations must be made. The guideline in making simplifications is to consider what physical features of the fluid flow have non-negligible effect on maximum slamming-induced structural stresses.

Slamming can also be connected with green water on deck. This phenomenon occurs when compact masses of water enter the ship deck. They can then evolve along it, hit obstacles on their way and slosh in zones with deck protections (i.e. bulwarks). The probability and severity of such phenomenon is larger for severe sea conditions and incoming wavelengths comparable to the ship length. The features and consequences depend on the incoming waves (wavelength, steepness, heading), on the vessel type and on its operational conditions (loading conditions, without/with forward motion). Floating production storage and offloading (FPSO) ships recorded several accidents with relevant local damages associated with slamming due to shipped water. This is particularly critical for vessels with deck house in the bow region.

The analysis of green-water occurrence and severity is rather difficult due to the complex phenomena possibly involved and the intrinsic nonlinear behaviour. In the case of FPSO vessels, model tests by Buchner (1995) identified the dam-breaking (DB) type event as typical shipping scenario. In this case the shipped water propagates along the deck similarly as the flow generated after the breaking of a wall limiting a reservoir of liquid (dam). MARINTEK (2000) experiments recorded also less common plunging-wave (PW) type water shipping. In this case the water invades the deck in the form of a large scale plunging wave able to hit directly the deck house in the forward part of the vessel before wetting the deck. In the real circumstances one can expect that the possible water-on-deck scenarios can be more complex and share partial features of the two mentioned types or can be characterized by other behaviours.

A more specialized but challenging problem is launching of free-fall lifeboats from offshore platforms which has created attention in Norway due to the economic consequences of operational limits. Safe launching must be possible in as high sea states as possible. The concern is slamming loads as well as acceptable accelerations for the passengers. The design constraints of the lifeboat are, for instance, sufficient volume for the passengers, small weight and good propulsion.

We will first focus on external slamming on ships, platforms and subsea modules and then discuss sloshing-induced slamming with focus on prismatic LNG tanks.

2 External ship slamming

Slamming on ships is categorized as bottom slamming, bow-flare slamming, bow-stem slamming and wet-deck slamming. Slamming can also occur as a consequence of breaking waves hitting the ship sides. Secondary impact due to flow separation during water entry should also be considered. Studies are often limited to head sea. However, the fact that the roll angle can be an important parameter implies that more attention should be given to oblique sea. Structural damage in oblique sea due to bow-flare slamming has been reported by Yamamoto et al. (1985). Large-amplitude rolling was an important contributing factor. The classical slamming theories by von Karman (1929) and Wagner (1932) are still very useful for vertical water entry of symmetric 2D bodies. Viscosity has a secondary effect during water entry, but may be important during water exit if the body is initially sufficiently submerged. The criterion for viscous effects to matter is viscous flow separation which takes time to develop for a body without sharp corners.

2.1 Boundary element method (BEM)

A 2D BEM with a jet-flow approximation was presented by Zhao and Faltinsen (1993) for water entry of a rigid body without gas cushion and flow separation. Gravity was neglected. Irrotational flow of an incompressible liquid with exact nonlinear free-surface conditions is assumed. A cut perpendicular to the body surface was made in the jet flow region close to the spray root. The latter technique avoids the numerical difficulties in finding the intersection between the free surface and the body surface for small local deadrise (impact) angles. Because the pressure can be approximated as atmospheric at the cut, the usual free-surface conditions apply at the cut. Zhao and Faltinsen (1993) presented also numerical results by applying Dobrovol’skaya’s (1969) similarity solution for vertical entry with constant velocity V of a semi-infinite upright wedge without gravity effect. Potential flow of an incompressible liquid is assumed. A similarity solution implies that the solutions of e.g. non-dimensional pressure and force can be represented in terms of non-dimensional variables without any explicit time dependence. For instance, the non-dimensional pressure Cp = ( p - pa)/(0.5rV2 ) on the body surface is a function of only the deadrise angle b and z / (Vt). Here pa is the ambient air pressure, r is the liquid density, t=0 corresponds to initial impact time, z is a vertical coordinate of the body surface and z= _Vt is the vertical coordinate of the wedge apex relative to the undisturbed free surface. Numerical results for deadrise angles between 4º and 81º showed very good agreement between the described BEM and the similarity solution. Both calculation methods are numerically challenging for small deadrise angles. A composite solution combining Wagner’s outer and spray-root domain solutions is more robust and provides the asymptotic limit when b → 0. The similarity-solution results represent valuable benchmark data for CFD solvers even though the Navier-Stokes equations are the governing equations instead of

Slamming on ships and marine structuresOdd M. Faltinsen


the Euler equations. The reason is that viscous effects play a negligible role during water entry. There exists a broad variety of CFD methods. Some methods use approximate free-surface capturing methods such as the volume-of-fluid, level set and color-function methods. Verification and validation are basic requirements. Verification involves benchmark testing, convergence studies and satisfaction of global conservation of mass, momentum and energy. Two examples involving comparisons with the similarity solution will be mentioned. Two master students independently used two different commercial CFD codes. Each student used only one of the computer codes. Both of the CFD codes were based on the finite-volume method to solve the governing equations and the volume-of-fluid method to capture the free surface. Since human errors due to the user happen, the names of the commercial computer codes are omitted. In one case good predictions were obtained for very low deadrise angle while the other student obtained good results only for deadrise angles larger than 45 degrees. A small deadrise angle is challenging for a CFD code. The rapid change of the flow at the spray roots requires locally small cells/elements or many particles depending on which numerical method is used.

When plunging breaking wave impacts on the underlying free surface, a BEM has difficulties. It is possible to account for non-viscous flow separation in a BEM. Zhao et al. (1996) showed how to account for flow separation from sharp corners. Comparisons were made with experimental results. A challenging problem during water entry is ventilation which may cause non-viscous flow separation from curved body surfaces. An example is during water entry of bulbous sections. Rolling and transverse velocity of ships combined with water entry can also cause flow separation. Sun and Faltinsen (2007) studied numerically the free water entry of a rigid bow-flare ship section with strongly nonlinear free-surface effects. Gravity was included. The effects of the roll angle on the forces and pressure distributions on the ship section were investigated by a BEM with exact free-surface conditions within potential flow theory without surface tension. The non-viscous flow separation model is described in detail by Sun and Faltinsen (2006) and involves detecting pressures smaller than the atmospheric pressure on the body surface next to the free surface. The procedure can be summarized as follows. The flow is first considered attached and it is investigated if negative pressures occur in a region downwards from the intersection between the free surface and the body surface. The negative pressures indicate ventilation and that the corresponding surface area should be separated. When starting the flow separation, a local analytical solution form of the separated free surface near the separation point as described by Zhao et al. (1996) is applied. An example in terms of calculated free surface elevations at two instants is presented in Figure 1 for a bow-flare section with constant heel angle 22.5º. Part of the calculations involves solving the nonlinear vertical body motions. Non-viscous flow separation occurs from the curved surface on the leeward side creating a ventilated area. There is also initially flow separation with secondary impact on the windward side causing an air cavity. The effect of the compressibility of the air cavity is not accounted for.

Fig. 1 Vertical water-entry. Simulation of non-viscous flow separation from the curved surface of a heeled bow-flare section with a boundary element method.

Sun and Faltinsen (2009) found, for the ship section studied, the vertical forces did not change much with the roll angle when the roll angle was small, whereas the horizontal force clearly increased with increasing roll angle. As the roll angle becomes larger, there will be a stronger impact on the flare surface, which can cause very high localized pressure in the flare area; the latter effect may cause hydroelastic effects. Non-viscous flow separation from the section bottom can occur for large roll angles. Flow separation significantly influences the pressure at the section bottom while the free-surface elevation and pressure distribution on the windward side are not apparently affected. Comparisons between the calculations and the model test results by Aarsnes (1996) are affected by experimental bias errors, induced, for instance, by the oscillatory motions of the rig and the upward force effects of the elastic ropes.

The fact that experimental errors exist is often ignored when numerical calculations are compared with experiments. Both bias and precision errors may matter. Investigation of precision errors requires repetition of tests. Bias errors can, for instance, be due to 3D flow in experiments that were intended to be 2D. One procedure is to use endplates to achieve 2D flow. The latter fact implies that the size of the end plates should be investigated. Another technique is to measure on a midsection of a 3D structure with constant cross-section. The length-to-“beam” ratio may become too small at the end of the drop for the 2D assumption to be true. Here the “beam” refers to the breadth of the instantaneous water plane area (Zhao et al., 1996). Other examples on experimental error sources are presented in the later sections on wetdeck slamming on catamarans and sloshing-induced slamming pressure.



2.2 Generalized Wagner method

A motivation by Zhao et al. (1996) to develop a generalized Wagner method was that the nonlinear BEM by Zhao and Faltinsen (1993) is numerically challenging for small local deadrise angles which makes it difficult to use by non-specialists in routine engineering calculations. The Wagner and generalized Wagner methods require that the body surface is a single-valued function of a lateral coordinate and that the wetted body surface increases with time. The free-surface conditions in the generalized Wagner method are the same as in Wagner’s outer-flow domain solution, i.e. the dynamic free-surface condition is zero velocity potential. The differences between the two methods are due to the fact that the exact body-boundary condition is satisfied and that both hydrodynamic pressure terms in Bernoulli’s equation are kept in the generalized Wagner method. The two hydrodynamic pressure terms have a cancelling effect and are important in the spray root area. The generalized Wagner method can adequately predict the pressure peak in the spray root area at deadrise angles smaller than approximately 30 degrees. Wrongly predicted negative total hydrodynamic pressure is set equal to zero. The effect of non-viscous flow separation from sharp corners in 2D flow was investigated by Zhao et al. (1996).

Zhao and Faltinsen (1999) applied the generalized Wagner model with and without non-viscous flow separation to water entry of axis-symmetric bodies. Faltinsen and Chezhian (2005) further developed the generalized Wagner model for 3D flow and validated the method by comparing with drop tests of the model illustrated in Figure 2.

The rise-up of the water differs along the body surface. The model has semi-circular cross-sections, fore-an-aft symmetry and a length-to-beam ratio of two. Each end part represents one fourth part of a spherical surface. Trim angles 0 and 10 degrees were studied. The model was supposed to be rigid. However, secondary local hydroelastic effects were present due to the very large impact loads occurring initially on a circular cross-section and due to the insufficient structural stiffening. A simplified theoretical model was set up to explain this fact in the experimental results. Clear 3D flow effects were demonstrated at the model ship ends.

It is not clear how to apply the 3D generalized Wagner method to ship bow geometry in a scenario with forward speed and incident waves. Two examples are illustrated in Figure 2. One case represents a steep wave impacting the bow stem of a passenger ship’s bow. The other case is a ship with bulb and

flare. The flow is likely to separate at the bulb in the vicinity of the line A1-A2 shown in the figure 2. The consequence is secondary impact on the flare section. 3D flow may prevent entrapped air to occur as a consequence.

A 2D generalized Wagner model is of common use in engineering studies (see e.g. Tuitman, 2010). The strips used for the 2D calculations do not necessarily coincide with ship cross-sections. For instance, 2D sections perpendicular to the bow-stem line may be chosen for the corresponding scenario of Figure 2. Tuitman (2010) leaves it up to the user to specify the location and orientation of the slamming sections. Possible flow separation at the bulb is not accounted for by creating artificial slamming sections with monotonically increasing width for an increasing submergence of the slamming section.

2.3 Local hydroelastic response

Hydroelasticity implies that the analysis of the hydrodynamic flow and structural reaction in terms of deflections and stresses cannot be separated. There is a mutual interaction whereby the structural vibrations cause hydrodynamic loads and vice-versa. Theoretical and experimental slamming studies related to drop tests of horizontal elastic plates of steel and aluminium are reviewed by Faltinsen (2005) (see also Faltinsen et al., 1997). The asymptotic theoretical model by Faltinsen (1997) involves a free-vibration phase succeeding a structural inertia phase that is asymptotically short relative to the highest natural structural period. The associated natural structural mode is of main importance for the resulting maximum structural stresses. During the initial phase, the pressure loads from either the water or an air cushion balance the structural inertia force of the plate, i.e. the elastic deformations w and associated bending stresses are negligible. A beam model with different end conditions was used to analyze the structure. The vertical velocity of the plate is expressed as where V is the downwards rigid-body velocity. The plate experiences a large force impulse during a small time relative to the highest wet natural period Tn1 for the plate vibrations in the structural inertia phase with the result that the elastic vibration velocity tends to the downwards rigid-body velocity in a space-averaged sense, i.e.

. Further, the plate surface is totally wetted at the end of the structural inertia phase. The space-averaging is done within a modal approach. The hydrodynamic impact is over at the end of the structural inertia phase. The initial conditions for the free-vibration phase is w = 0 and . The maximum stresses occur during the free vibration phase at Tn1 / 4. The hydrodynamic pressure is at the free-vibration phase associated with generalized added mass effects and is positive on the plate approximately until Tn1 / 2. The subsequent negative pressures can, depending on the impact velocity, be so large in magnitude that the



Fig. 2 Left: Drop test arrangement. Right : Two scenarios that the 3D generalized Wagner method cannot handle properly at present.

total hydrodynamic pressure becomes equal to the vapour pressure which implies cavitation. Because the impacting plate will have a small submergence when cavitation happens, the consequence is ventilation, i.e. air gets under the plate and the plate oscillates like it is in air. The possibility of both cavitation and ventilation was experimentally documented in the studies reviewed by Faltinsen (2005). The maximum stresses are, as a consequence of the initial conditions for the free-vibration phase, proportional to V, i.e. not to V 2 as it would be by quasi-steady theory. It was documented experimentally that maximum impact pressures and maximum stresses were uncorrelated. The latter fact is also a consequence of the described theory. The experimentally documented maximum impact pressure for a given impact velocity showed a large variation in repeated experiments which involved both calm-water impact and impact with varying wave conditions and impact position on the plate. Impact pressures as high as 80 bar were measured with a drop velocity of 6 m/s. If the size of the pressure gauges had been even smaller, even higher pressures may have been measured. The measured maximum stress was not sensitive to the impact scenario. The measured maximum non-dimensional strain amplitude at a given plate position was presented non-dimensionally as a function of . Here em is the strain amplitude, za is the distance from neutral axis to strain measurements, EI is the bending stiffness in dimensions N 2m2m

_1, L is the plate length and r is the mass density of water. Results for aluminium and steel and different values of L/R were presented with R being the radius of curvature of the waves at the impact position. Initially flat water, i.e. R=∞, was also included. The experimental results decrease slightly with decreasing non-dimensional impact velocity. If the largest L/R value of 0.198 is disregarded, the maximum strain shows small influence of L/R. The largest L/R value is normally unrealistic for slamming. Because the maximum stress does not depend on the details of the hydrodynamic flow during impact, only Froude scaling, geometric similarity and scaling of important natural structural frequencies matter in model tests when the theory is applicable.

Faltinsen (1999) studied the relative importance of hydroelasticity for an elastic hull with wedge-shaped cross-sections penetrating an initially calm water surface (see Figure 3). Stiffened plating between two rigid transverse frames was examined.

Fig. 3 Above: Water entry of elastic hull with wedge-shaped cross-section. Below: Stiffened plating consisting of plate and longitudinal stiffeners between two transverse frames.

A hydrodynamic strip theory in combination with orthotropic plate theory was used. Wagner’s theory was generalized to account for elastic vibrations. The water entry velocity was assumed constant. The non-dimensional parameter was introduced. L is the length of the analysed longitudinal stiffener between the two transverse frames. EI is the bending stiffness per width of the longitudinal stiffener including the effective plate flange. The parameter x is proportional to the ratio between the wetting time of the rigid wedge, i.e. the load duration Td , and the highest natural period Tn1 of the longitudinal stiffener. The theoretical behaviour of the dominant mode is similar as for a mass-spring system with a transient load of duration Td and natural period Tn1.

Fig. 4 Non-dimensional maximum strain em in the middle of the second longitudinal stiffener from the keel for different non-dimensional constant impact velocities VND.b = deadrise angle. Calculations by hydroelastic orthotropic plate theory (Faltinsen, 1999) are shown.

Non-dimensional strain results are presented in Figure 4 as a function of x. There are also presented results based on quasi-steady analysis and asymptotic hydroelastic analysis for small deadrise angles b. The quasi-steady analysis assumes the structure is rigid in the hydrodynamic calculations. The pressure is then proportional to V 2. The quasi-steady analysis of the structural deformations due to the water impact gives that is independent of the abscissa in Figure 4 and corresponds to the asymptotic behaviour when x → ∞. The asymptotic hydroelastic analysis for small x_ values is based on Faltinsen’s (1997) hydroelastic analysis and appears as a straight line in Figure 4. The particular way of non-dimensioning the results gives small explicit dependence on the dimensionless impact velocity

. Figure 4 illustrates that hydroelastic effects are present when for the studied stiffened plating. The stress from the hydroelastic case may also exceed the stress from the quasi-steady case. A large influence of hydroelasticity occurs when

r e su l t ing in c l ea r ly sma l l e r



maximum stresses than predicted by quasi-steady theory. By independently varying terms in we see that small x-values are obtained when a) the deadrise angle b is small, b) the water entry velocity V is large, c)

is large which corresponds to large value of the highest wet natural period. A very rough guidance is that local hydroelastic effects ought to be considered when the local deadrise angle between an impacting free surface and the body surface is less than 5 deg.

Sun and Faltinsen (2006) studied the water impact of an elastic cylindrical shell by coupling a BEM for the water flow and a modal analysis for the structural responses. It was shown that the initial water impact, the flow separation from body surface and the ventilation near the free surface can affect the structural responses at a later time of the water impact.

2.4 Global slamming effects on monohulls

The global slamming effects on ships (whipping) may involve hydroelasticity. The latter is, for instance, true for container vessels. A combination of springing and whipping may occur where springing is defined as wave-excited resonant steady-state hydroelastic vibrations. Linear as well as higher-order nonlinear body-wave interaction effects can excite springing (Shao and Faltinsen, 2012a). Since the dominant natural springing frequency is high, the wave radiation damping is small. Hull-lift damping can contribute. Since a major damping source is structural damping, it is difficult by rational methods to assess the damping level. Global hydroelastic response analysis involves combining the hydrodynamic analysis with a beam model or a 3D dynamic Finite Element method for the ship structure. Hydrodynamic effects occurring on a time scale much smaller than the highest global wet natural elastic structural period, such as water compressibility and local hydroelasticity, can be neglected.

Fig. 5 Time histories of the loads, motions and accelerations at λ/L = 3.0 and wave amplitude ζa=0.0555B with = 1.78 and τ = 4º. Acc. means the acceleration. τ = trim angle.

Ideally the slamming predictions should be fully integrated in the wave-induced response analysis. An analysis like this

was done by Sun and Faltinsen (2011) for a rigid planing vessel. A nonlinear 2D+t method was used to calculate heave and pitch in regular head sea waves. 3D corrections at the transom stern were applied. The motivation for the corrections is that the pressure has to be atmospheric at the transom while the pressure predicted by the method depends only on upstream effects. The 3D corrections were done by setting the sectional force equal to zero either over a distance 0.25B or 0.5B from the transom. Here B is the beam. The ship motions are affected by the 3D corrections, especially near the resonance frequency, while the phase angles are slightly affected and the acceleration peaks at the bow near the resonance frequency are sensitive to the 3D corrections. Nonlinearities are clearly present in the studied case which can be seen from the numerical time history presented in Figure 5 where we, for instance, see periodic sharp peaks. The incident wavelength-to-ship length ratio is chosen as λ/L=3.0, because the maximum non-dimensional heave and pitch amplitudes appear at about this wavelength. No 3D correction is applied here. The non-dimensional hydrodynamic vertical force F3* and pitch moment F5* are normalized by ρU2B2 and ρU2B3, respectively. Here U is the ship speed. The accelerations at the COG and at the bow, with a distance of 10%L from the stem, are also presented. The accelerations are made non-dimensional by g, the acceleration of gravity. The direction of the acceleration at the COG is normal to the calm water surface and the acceleration at the bow is normal to the keel. The reason of the sharp peaks in the time histories of the pitch moment and the acceleration at the bow is analyzed. From the numerical results we can see the following phenomena. When the bow meets the front wave slope, the wetted-length of the keel rapidly increases. At the same time, the bow is going downwards, so the bow impacts on the wave surface and causes a rapid increase in the vertical force on the bow. Although the vertical force on the stern is also increasing, the contribution from the bow to the pitch moment is greater. This results in a fast increase in the positive pitch moment. Afterwards, the downward speed of the bow is quickly decelerated, so the force in the bow decreases, however, the force in the stern is still increasing. Therefore, the pitch moment rapidly decreases but the total vertical force does not change much. The sharp peak in the pitch moment will then influence the pitch acceleration and therefore cause a sharp peak in the acceleration at the bow. It can be seen in Figure 5 that there are small sharp peaks in the total vertical force and the acceleration at the COG at the same time instants, but the peaks are not as prominent as for the pitch moment and the acceleration at bow.

A CFD method can provide fully integrated 3D analysis of global slamming response with nonlinear free-surface effects. Recent examples on coupled CFD and structural analysis of whipping and springing of displacement ships are provided by El Moctar et al. (2011) and Oberhagemann and el Moctar (2012). Possible slamming loads on a nearly flat overhang at the transom can be accounted for. The latter problem has similarities with wetdeck slamming. However, a CFD method is too computationally demanding to properly simulate the effect of design sea states.



Simplifications have to be made in engineering analysis. Tuitman (2010) simplified the slamming loads and used the 2D generalized Wagner model for monohulls. Nonlinear Froude-Kriloff and hydrostatic restoring terms are added and combined with a linear elastic ship-motion model in the time domain by means of convolution integrals involving retardation functions which can be evaluated by means of either the generalized frequency-domain added mass coefficients or damping coefficients. Because many pragmatic theoretical simplifications are used, comparisons with model and full scale tests are a must. There exist many different ways to solve the linear hydrodynamic problem in an analysis similar as described by Tuitman (2010). Ideally one should include the interaction between the local steady and unsteady flow along a ship. An inertial coordinate system is common to use. The consequence is the so-called mj-terms in the body boundary conditions associated with the fact that the steady flow problem does not satisfy the boundary condition on the instantaneous ship position. Because second order derivatives of the steady flow potential are involved in the mj-terms, numerical difficulties arise. Since the formulation is based on a Taylor expansion requiring an analytical solution of the velocity potential, the procedure fails at sharp corners with interior angles less than 180o, e. g. bilge keels and rectangular cross-sections. The mj-terms are avoided if a body-fixed coordinate system is used (Shao and Faltinsen, 2012b).

Further studies are needed to incorporate slamming as a fully integrated part of the calculation of wave-induced ship response in a time-efficient way and such that e.g. 3D flow and forward speed effects are correctly accounted for. It is appropriate to assume potential flow of incompressible water in such an analysis. However, using state-of-the-art nonlinear BEM is presently too time-consuming. We are now working on developing a more time-efficient potential flow solver which we have called the Harmonic Polynomial Cell (HPC) method. It implies that the water domain is divided into overlapping cells. In each cell a complete set of polynomials that satisfy Laplace equation is used. Exact nonlinear free-surface conditions can be satisfied. The method has been shown to be very time efficient and accurate for idealized problems (Shao and Faltinsen, 2012 c). However, there is some way to go before we can prove the efficiency and accuracy in concurrent modeling of waves, ship motions, slamming loads and structural responses.

2.5 Wetdeck slamming on catamarans

An accident involving wetdeck slamming happened 24 March 2010 with the high-speed catamaran MS “Sollifjell” in Norway. A drawing of a longitudinal cut of the wetdeck is shown in Figure 6. The wetdeck is flat in the cross-sectional plane. The design of the front panel of the wetdeck was special. It had an 45o angle relative to the rest of the wetdeck. The consequence is that the forward speed can contribute significantly to the relative impact velocity on the front panel and thereby to high loading on the front panel. The loading on the front panel may have initiated the damage on the rest of the wetdeck.

Fig.6 Above: Illustration of the wetdeck of MS “Sollifjell” containing a 45o front panel. Below: Outline of the experimental hull arrangements, top view (Ge, 2002).

Design procedures of wetdecks considering the slamming load effects have to be improved. The details of the vessel dynamics as well as the slamming load effects have to be accounted for. The wetdeck geometry (bow ramp angle, deck flatness etc.) and material ought to be reflected in the rules. Aarsnes and Hoff (1998) presented full scale experiments of wetdeck slamming on a 30m long catamaran. The measured maximum strain corresponded to about half the yield stress. This occurred in head sea with significant wave height H1/3=1.5 m and ship speed 18 knots. The ship was allowed to operate up to H1/3=3.5 m. The classification rules did not predict well that the ship had sufficient height of the wetdeck above sea level to avoid wetdeck slamming. It should be investigated if simple formulas in the rules for sufficient height of the wetdeck above sea level could be exchanged by direct simulations with state-of-the-art computational tools that properly predict the hydrodynamic effects on the trim angle which is an important parameter for wetdeck slamming on high-speed vessels.

Theoretical predictions of global wetdeck slamming effects on a catamaran at forward speed do not need to be complicated. Ge (2002) and Ge et al. (2005) studied global hydroelastic wetdeck-slamming response of a catamaran in head-sea regular waves at forward speed by theory and using published experiments. The vessel model used in the experiments is shown in Figure 6. The overall length is 4.1 m. Each side hull consists of three rigid sections. The hull sections are connected by steel springs and aluminium transducers longitudinally and transversely. These elastic connections are then modelling the global elastic behaviour of a catamaran. However, this can only be approximate. The wetdeck consists of four rigid flat sections. The transverse flexibility between the two hulls was not accounted for. A reason for neglecting the transverse connecting springs and beams is that long-crested head sea waves are considered. The linear hydrodynamic loads on the sidehulls were based on generalizing the Salvesen-



2.6 Offshore platforms and VLFS

Both the global longitudinal and vertical slamming forces on offshore platform decks are of concern. The described theoretical global wetdeck slamming model for a catamaran at forward speed will not be similarly accurate for wetdeck slamming on an offshore platform. Baarholm and Faltinsen (2004) reported experimental and numerical studies of slamming on a fixed horizontal deck above the mean free surface with 2D flow conditions and incident regular waves. As the wave hits the front end of the deck (see Figure 7), the wetted length increases smoothly, and a pile-up of water and a thin jet are formed on the upstream side of the model. Compared with the undisturbed wave, a considerable propagation of water downstream of the wetted body caused by the impact will be present. Later, the upstream body/free-surface intersection moves around the front corner to the bottom plate of the deck which is likely to cause viscous flow separation at the front corner. The free surface near the intersection is characterized by high curvature. As the flow reaches the aft end of the deck, the water flow leaves the deck tangentially. Spray and wave breaking behind the body dissipate energy. After some time, the downstream intersection starts to move forward again, and finally the water detaches from the deck with a highly peaked and narrow free-surface shape. The minimum negative vertical water exit forces are of similar magnitude as the maximum vertical water entry forces.

Fig.7 Slamming on stationary horizontal deck. Above: Single impact event in left part. Below: Multiple impact events.

Tuck-Faltinsen strip theory to account for three rigid bodies. Hydrodynamic interaction between the side hulls was neglected and the linear load expressions were kept in the frequency-domain with a specified frequency of encounter. Since the considered problem is transient of nature and involves response at the natural frequencies in heave and pitch and at least the natural frequency associated with a two-node longitudinal bending mode, it is a simplification to consider only the linear hydrodynamic loads at one frequency. Ideally one should have time-domain representation of the linear hydrodynamic loads in terms of convolution integrals. The wetdeck “slamming” model included both the water entry and exit phase and was based on a 2D von Karman method with additional nonlinear Froude-Kriloff and restoring terms. A Wagner model cannot be used during water exit. Because the vessel has a forward speed and the water impacts in the forward part of the wetdeck, the ship flow effect on the relative water impact velocity is negligible. The vertical wetdeck force is roughly speaking positive during the water entry phase (increased wetted area) and negative during the water exit phase (decreased wetted area). The reason for the negative force during the water exit can be explained by considering the force part . Here A33 is the infinite-frequency heave added mass associated with the wetted deck area and is the vertical acceleration of the incident wave at the wetted deck relative to the vertical acceleration of the catamaran at the same position. is negative during the water exit which explains the negative force. The maximum vertical wetdeck force during water entry and minimum vertical wetdeck force during water exit are similar in magnitude. The duration of the water entry and exit phases are similar. Considering only the water entry phase would lead to erroneous answers. A simple way to understand this fact is to consider the transient heave and pitch response. Because the natural heave and pitch periods are more than four times the wetdeck load duration, it is the force impulse that matters. The theoretical “slamming” model showed good agreement with experimental force results during the model tests in regular head sea waves, indicating that all the fine details of the “slamming” pressures were not important.

The theoretical and experimental values of the vertical shear force and bending moment at the two cuts were in reasonable agreement and showed clear hydroelastic effects due to wetdeck slamming. An assessment of relative errors in the experimental shear forces and bending moments was made. A first step was to assess experimental error sources and use the computer program to find the resulting relative errors in global loads. The following error sources were found to be important: a) changing incident wave amplitude along the track of the model, b) wave measurements, c) unintented roll, sway and yaw due to asymmetry of the hull relative to the centreplane of the catamaran, d) trim, e) wetdeck geometry. The most important error source was found to be trim. Examples of estimated relative errors in experimental maximum vertical shear force at cut 1 and 2 are 0.18 and 0.26, respectively. The correponding relative errors for vertical bending at the the two cuts are 0.29 and 0.17. It is very likely that the estimated errors would be smaller if the experiments had been done simultanously with the theoretical investigations. For instance, more emphasis had been put on accurately measuring the trim angle.


28 Marine Systems & Ocean Technology Vol. 8 No. 1 pp.21-37 June 2013

A difference occurs for subsequent impacts (see Figure 7). The disturbance of the free surface caused by the preceding impact process causes a double slam event where the second impact occurs in the vicinity of the final detachment of the preceding wave. This gives a significant positive force peak of short duration. In reality, 3D flow effects , e.g. due to wave radiation and diffraction, are important for large-volume structures such as semisubmersibles and gravity platforms. Further, current-wave interaction can play an important role for the impacting wave field.

Wave runup along the columns can cause local damage to the wetdeck. It is theoretically challenging to predict the run up. A special phenomenon was experimentally detected for a single column in survival conditions in deep water. The objective was to understand the hydrodynamics of ringing which is transient global elastic response due to higher-order wave-body interaction causing superharmonic excitation loads. The column dimensions were representative for the Draugen mono-tower gravity platform in the North Sea. Very local steep waves due to wave-body interaction that propagated in the incident wave direction developed on the two sides of the column. The local waves resembled hydraulic jumps. They started on the upstream side and collided on the downstream side with consequent large vertical water flow that could hit a platform deck. One has to the author’s knowledge not been able to theoretically predict the flow.

Local and global slamming effects on columns have to be considered in incident steep waves which matter particularly in shallow-water condition. The slamming loads may until non-viscous flow separation happen be approximated by Wagner theory as long as the wetted height-to-wetted breadth ratio is large in order for strip theory to apply. Further, we should strictly speaking require that V t / R is small. Here V is the impact velocity, R is the cylinder radius and the time t=0 corresponds to initial impact.

The behavior of bottom slamming on a pontoon-type VLFS with only a few meter draft has similarities with the initial behavior of the deck slamming shown in Figure 7. The length and breadth of a VLFS planned as a floating airport are, e.g., 5000m and 2000m, respectively. Figure 8 shows the pressure evolution measured by Yoshimoto et al. (1997) on a fixed pontoon-type model in incident waves together with numbers that identifies different phases of the flow by drawings (Greco et al., 2009). The run-down phase (1) is responsible for a pressure reduction leading to values even lower than the atmospheric pressure during the water turning around the upwave edge of the platform bottom (2). This initiates the water-exit phase of the VLFS. Once the water front has passed the pressure probe, the structure becomes dry there and is subjected to atmospheric pressure (3). This lasts until the water starts to rise again and eventually impacts the platform bottom (4). As a result, a water-entry phase occurs and the water run-up in front of the upwave edge is responsible for an increase of pressure. The latter occurs when the impact loads have become negligible. A secondary relative maximum of the pressure occurs when the maximum run-up is reached by the water (5), then a new water run-down occurs again reducing the pressure level. Other scenarios may happen as a consequence of wave interaction

between the incident waves and the shallow-draft pontoon. For instance, an air cavity may be formed during bottom slamming. Another case is bow impact (see Figure 8). The described slamming may cause both local and global hydroelastic events.

Fig.8 Pressure measurements by Yoshimoto et al. (1997) at location P-1 and physical interpretation from the numerical analysis (Greco et al., 2009)

2.7 Subsea structures

Prediction of wave loads on subsea structures that are lowered or lifted by a ship through the splash zone can be a challenging problem. A reason is the geometrical complexity of the subsea structure. Marine operations as this are planned for the Aasgaard field in the North Sea in significant wave heights up to 4.5 meters. The desired high operating sea states are a consequence of that a non-functioning module of a seabed gas compressor should be replaced with minimum economic loss for the gas production. Since the lowering/lifting velocity is small, both water entry and exit happens as a consequence of the relative motion between the ship and the waves. The local wave effects due to the ship are of particular concern if the operation happens through a moonpool with piston mode resonance. The piston-mode resonance period is typically of the same order as the heave natural period. There exist to the author’s knowledge no reliable theoretical prediction methods for water entry and exit loads on geometrically complicated subsea structures. A simplified method as previously described for wetdeck slamming on catamarans can be used for preliminary estimates. That means one consider nonlinear Froude-Kriloff and hydrostatic restoring terms in combination with a von Karman method that involves the time derivative of the product of added mass and relative inflow velocity. The added mass as a function of time can be calculated by a 3D BEM with a high-frequency free-surface condition. There exist commercial programs that simulate the complete marine operation including water entry and exit. However, their water entry and exit loads are in terms of constant water entry and exit coefficients which do not reflect the time variation of the loads. Further, a question is how to know these coefficients. In reality, model tests are needed to simulate the marine operation in the free-surface zone by considering incident waves as well as the presence of the ship.

2.8 Green water

A systematic and comprehensive description of the green water-on-deck phenomena is provided by Faltinsen and Greco (2011) on the basis of experiments and of 2D numerical simulations


Vol. 8 No. 1 pp.21-37 June 2013 Marine Systems & Ocean Technology 29

based on a BEM and on a field method solution. The main water-shipping scenarios were identified as: dam-breaking (DB) type, where the shipped water propagates similarly as the flow generated after a dam breaking with high velocities along the deck, which may be as high as 15m/s at large relative vertical ship motions; plunging-wave (PW) type, where the water invades the deck in the form of a large scale plunging wave hitting the deck or superstructures; initial plunging plus dam breaking (PDB) type, where the water enters the deck in the form of a small scale plunging wave hitting the deck near the bow and then propagates as in a DB event; hammer fist (HF) type, where a nearly rectangular-shaped liquid mass rises obliquely above the deck and then splashes violently against it. The PDB appeared as the most common scenario, PW and HF the less common but also potentially the most severe. All types of water shipping can lead to water impacts against obstacles on the deck. The PDB, PW and HF cause also impacts against the deck and lead to more or less pronounced air entrapment which can affect the resulting green-water loads. From the study, in general the numerical analysis of green-water occurrence and severity appears rather difficult due to the complex phenomena possibly involved and the intrinsic nonlinear behavior.

The DB large-scale features can be simulated coupling a suitable seakeeping solver with a shallow-water approximation for the in-deck liquid evolution, as shown by the numerical and experimental studies by Greco and Lugni (2012) and Greco et al. (2012). The adopted solver combines a weakly nonlinear external solution for the wave–vessel interactions with a 2D in-deck shallow-water approximation, and a local analytical analysis of the bottom-slamming phenomenon. It can handle regular and irregular sea states and vessels at rest or with limited speed, expected in rough seas. The solver was compared with 3D model tests of a patrol ship at rest or small forward speed in head-sea regular waves. From the investigation the wave-body interactions can lead to slamming loads with different features depending on the location of the impact: on the hull bottom, the pressure evolution was typically characterized by a church-roof behavior, with the first short peak due to the water impact against the structure and the second mild rise due to wave-reflection effects; on the ship deck, the pressure has a double-peak behavior near the superstructure, with the first peak due to a water-wall impact and the second peak caused by water falling and impacting on underlying water, and a single-peak behavior near the bow, due to the new water entering the ship deck; on the side hull, the pressure has a church-roof behavior for mild conditions and a double-peak behavior for severe conditions.

To handle general water-on-deck scenarios the shallow-water approximation is not suitable and numerical methods able to handle breaking and fragmentation phenomena are needed. On the other hand, the state-of-the-art solvers are not able yet to provide accurate results and reliable statistical investigations of the local and global green-water loads in the case of realistic geometries due to the demanding memory-space and CPU-time requirements. A compromise between capability, accuracy and efficiency could be represented by hybrid methods based on Domain-Decomposition (DD) strategies, where the problem solution is split in time and/or in space among different solvers.

Each solver is chosen as the most efficient among those accurate and capable which are available. Recent attempts in this direction are represented by the 2D work of Colicchio et al. (2011) handling also air entrainment, and by the 3D investigation of Colicchio et al. (2010).

3 Sloshing-induced slamming Sloshing-induced slamming in membrane tanks with LNG is more complex than the previous applications. The reasons are a) sloshing involves violent liquid motions, b) many flow parameters have to be recognized, c) the membrane structure is far more complex than steel structures, d) the fine details of an impacting free surface may matter for a membrane structure and lead to stochastic behavior even for deterministic tank motion.

CFD has limitations which reflect the fact that model tests are the basis in design. However, model tests are also limited due to the fact that all fluid dynamic and thermodynamic parameters that may be important are not considered. Further, the tank model is normally assumed rigid. It is challenging to properly model the structural properties of a membrane tank in model scale. Model tests of slamming and sloshing are typically done with prescribed tank motion which may be found by calculations as a realization of the ship motions in representative sea states. The calculations must account for the mutual interaction between ship motions and sloshing. The 2D numerical calculations and experiments by Rognebakke and Faltinsen (2003) illustrate the mutual interaction between sloshing and wave-induced ship motions and the fact that nonlinear sloshing matters. The external flow can to a large degree be based on linear potential flow for sea states causing violent sloshing. However, nonlinear viscous roll damping must be accounted for. The sloshing effects ought to consider nonlinear effects which can cause 3D flow such as swirling, diagonal waves and chaos in prismatic tanks with length-to-breadth ratio around one (Faltinsen and Timokha, 2009). The latter can occur even though the forcing is along a tank wall. A linear theory will then only account for 2D flow. Tank roof impact may also affect the global sloshing induced forces and moments (Faltinsen and Timokha, 2009). Even though CFD is not recommended in general for sloshing-induced slamming, it may better describe the global effect of sloshing. However, the computational speed of CFD methods make it in practice unrealistic for long time simulations in a sea state. The nonlinear multimodal method (Faltinsen and Timokha, 2009) is a fast method which from a CPU point of view can realistically simulate the effect of a sea state. Assumptions are potential flow of an incompressible liquid without overturning waves. 3D effects can be considered. However, the method has not been developed to the stage where it can be used in engineering calculations. One drawback is the difficulties in handling shallow liquid cases with realistic tank excitation



amplitudes. Then we are left in practice with linear sloshing theories which are fast and are commonly used. What errors are caused in slamming induced structural stresses by using calculations of tank excitations as a basis for model tests should be investigated. An issue is also the statistical analysis of the response.

Many possible impact situations have to be considered. For instance, large filling ratios can cause important slamming loads on the tank roof. An example is impact of a nearly horizontal free surface. Another case is impact where the geometry of the impacting free surface causes a gas cavity as it is illustrated from experiments in Figure 9. A gas cavity has a natural frequency associated with the compressibility of the gas and a generalized added mass due to the liquid oscillations caused by the gas cavity oscillations. Transient damped pressure oscillations in the gas cavity are excited by the impact.

Fig.9 Gas cavity associated with tank-roof impact.

Possible scenario at very large filling ratios is a sudden flip-through of the free surface at the tank wall. A vertical jet flow with a high velocity will, as a consequence, impact on the tank roof. A chamfered tank roof reduces the severity of slamming for large filling ratios.

Swirling in a nearly-square base tank is an example of 3D effects that may cause important impact against the tank roof corners for non-small liquid depths.

One must recognize that slamming does not only cause important loads in the impact area. For instance, if the adjacent tank wall is more flexible than the tank roof, significant stresses can occur as a consequence of the tank roof impact (Faltinsen and Timokha, 2009).

Steep waves impacting on a vertical tank wall represent an important scenario for shallow and lower-intermediate liquid depths. Hattori et al. (1994) studied experimentally impact pressures on vertical walls due to breaking waves and identified the following four conditions: (1) “flip-through” condition with no air bubbles; (2) collision of a vertically flat wave front with entrapment of small air bubbles. The impact pressure had a single peak; (3) collision of plunging breaker with a thin air pocket; (4) collision of fully developed plunging breaker with a thick air pocket. Damped impact pressure oscillations occur in conditions 3 and 4 with a similar behavior as for tank roof impact with a gas cavity. A comprehensive review is given by Peregrine (2003).

When the flip-through phenomenon occurs, the concave

face of the wave approaches the wall with the crest moving forward and the trough rapidly rising at the wall (Oumeraci et al., 1993). The presence of the wall delays breaking of the wave and causes the rise of the leading wave trough. The latter focuses with the wave front, giving intense acceleration to the flow and turning it in the focusing area to form a vertical jet. Very large pressures can occur in the flip-through condition. The high pressure loading on the tank wall is sensitive to small changes of an impacting steep free surface.

Lugni et al. (2006, 2010a, 2010b) studied experimentally sloshing-induced slamming on rigid tank walls in shallow-water conditions. The 2006-study focused on flip-through. The important role of the ullage pressure was investigated in the 2010-studies. A vacuum pump enabled changes in the ullage pressure between 1 bar, i. e. atmospheric pressure, down to 15 mbar. The impact scenario involved an air-cushion and it was documented that leakage from the air cushion had initially a large damping effect on the pressure oscillations due to the air cavity. Further, it was evident that the gas cavity oscillations could not be described at an initial phase by a single natural frequency following from linear theory.

3.1 Scaling of impact loads and resulting structural response

Because there are no numerical methods that can fully describe the sloshing-induced slamming pressures, one has to rely on experiments which means in practice model tests. The challenges are how to scale the model test results to full scale and properly account for the structural elastic reactions due to the fact that a rigid model is used in model scale.

The following discussion of scaling of the model-test results of maximum slamming pressure to a full scale is based on the Pi-theorem. However, we need also to know the spatial distribution of impact pressure as a function of time (Maillard and Brosset, 2009). We assume first a rigid tank and then examine hydroelastic effects. The tank is in the example forced harmonically with a period T and transverse motion amplitude ha. We assume that the maximum slamming pressure p at a certain point is a function of the following parameters: length, breadth or another characteristic length L of the tank, characteristic velocity U of the tank, e.g. L / T, liquid depth h, other pertinent tank dimensions Si , i = 1,2,..., N , kinematic viscosity n of the liquid, liquid density rl , ullage gas density ro, surface tension Ts , bulk modulus El of the liquid, ullage pressure p0 and liquid vapor pressure pv . It follows from the Pi-theorem that

(1)

Here is the Froude number, UL / n the Reynolds number, p0 / rlU2 the Euler number, rlU2 / E2 the Cauchy number, (po - pv)/ ( rlU2) the cavitation number and rlU2L / Ts

the Weber number. We can combine the above-mentioned cavitation number and the Froude number into the modified cavitation number Cn = (po - pv) / (rl gL) used by Olsen and Hysing (1974). Because the Froude number is kept the same



in model and full scale, Cv expresses the same physical effect as (po - pv)/ ( rlU2). Similarly, we can introduce the modified Euler number CE = po / (rl gL). If the gas-liquid volume fraction is zero, the speed of sound in the liquid is and we can rewrite the Cauchy number in terms of the Mach number Ma = U / c0 . The procedure can be generalized to any forced tank motion by introducing non-dimensional translatory tank motion with respect to L and by Froude scaling the time scale. Angular tank motions remain the same in model and full scale. Thermodynamic effects may also matter for LNG and NG. Further, hydroelasticity is of concern.

Only Froude and geometric scaling are traditionally considered important in model testing. Abramson et al. (1974) presented an example illustrating the importance of Froude scaling for slamming pressures. A number of pressure gauges were installed in an OBO tank carrying water ballast and pressures and roll were measured with different filling heights during a voyage from Japan to the Persian Gulf.

The effect of the surface tension is sometimes measured in terms of the Bond number instead of the Weber number. The Bond number BO = rl gL2 / TS is the Weber number divided by the square of the Froude number. It represents the ratio of inertia to surface tension forces and, if greater than 104, surface tension and associated meniscus effect with capillary wave generation can be neglected when modeling a free surface (Myskis et al., 1987). The Bond-number criterion implies that a tank model has to be very small for surface tension to matter. However, surface tension governs the size of gas bubbles mixed with liquid, i.e. LNG. Eigenfrequencies of gas bubbles depend on their radius. These frequencies contribute to time scales of hydrodynamic loads. The effect of the liquid viscosity is represented by the Reynolds number. We can combine the Reynolds and Froude numbers into the modified Reynolds number = L3/2g1/2

/n . The values of are very different in model and full scale. For both the Reynolds and Froude number scaling to be satisfied, the ratio between the length in model and full scale is given by Lm / Lp = (nm / np )2/3 for gm = gp, where the subscripts m and p indicate model and full scale (prototype), respectively. With realistic values of Lm / Lp it is impossible to find a model-scale liquid that satisfies the relationship. It means that we cannot properly describe viscous effects in model tests. However, viscosity does not have generally speaking a dominant influence on slamming pressures and integrated hydrodynamic loads for a clean tank (Faltinsen and Timokha, 2009).

Maillard and Brosset (2009) performed model tests with forced harmonic surge motions of a rigid rectangular tank filled either 81% or 90% with water and showed that the density ratio between the ullage gas and the liquid matters for the statistical values of the slamming pressure. Most presented statistical pressure values were based on using a return period of 1/10th of the total test duration. The statistical sample considers the maximum pressure irrespective of the sensor for a given impact. 2D flow conditions were attempted. The cavitation number was kept equal to zero in one of the test series by

varying the ullage pressure and temperature and by using water vapor as the ullage gas. The density ratio between gas and liquid varied from 0.00005 to 0.0058. The density ratio between natural gas and LNG within an LNG tank is around 0.004 depending on the quality of LNG and the temperature of the gas, while it is around 0.0012 during model tests with air and water at room temperature. Zero cavitation number is relevant for LNG. The vapor can condensate at zero cavitation number due to overpressure during impact. The condensation in LNG tanks may not be as quick as the condensation of water vapor according to Maillard and Brosset (2009). Another test series was done at atmospheric pressure with Helium to get a density ratio of 0.0005 and with different mixtures of Sulphur Hexafluoride and Nitrogen to get density ratios of 0.0036 and 0.0046. A third test series was at atmospheric pressure at different temperatures with air and density ratios from 0.0008 to 0.0012. The general trend in the test series is that the slamming pressure decreases with increasing density ratio. For instance, the decrease of the statistical pressure between a density ratio of 0.0012 and 0.0036 is around 50% for the tests with a non-condensable gas while this decrease is around 65% for the vapor tests. The authors’ argument is that a larger share of the energy is transferred from the liquid to the gas for a heavier gas than for a lighter gas and thereby reduces the impact velocity of the liquid. Their results at a density ratio around 0.004 show that it is conservative to assume atmospheric pressure conditions for the statistical slamming pressure. A main contributing factor to lower pressures with water vapor as a gas at high density ratios, e.g. 0.004, is believed to be condensation. Zero cavitation number at atmospheric pressure conditions can be achieved in model tests by boiling water. Olsen and Hysing (1974) presented experimental slamming pressure results with water at 20o, 95o and 100o and air as the ullage gas. If we use the tank breadth l as the characteristic length, the cavitation number Cv is 7.39, 1.29 and 0, respectively. The slamming pressure coefficient p / (rl gl)with a 10% exceedance level was presented as a function of the non-dimensional forcing period . The liquid depth-to-tank breadth ratio was h / l = 0.12 and h / l = 0.4 and the non-dimensional sway amplitude h2a / l was as high as 0.10. Because the different results for water at 20o show a variation comparable with the changes as a function of the cavitation number, it is difficult to conclude about the influence of the cavitation number. In other words such influence seems to be limited. We should also note that the Reynolds number is not the same for water at 20o, 95o and 100o.

Maillard and Brosset (2009) stated, based on their own experiments and numerical investigations by Braeunig et al. (2009), that the ullage pressure (and so the Euler number) is not an important parameter. However, the experimental variation of the ullage pressure at constant density ratio was small. A broader range of ullage pressure was obtained in the numerical studies. However, the impact flow was idealized by considering a liquid with initially rectangular shape and horizontal bottom falling downward and impacting on a rigid horizontal surface. A side comment is that the structure ought to be considered elastic in an impact scenario. It is shown by Faltinsen and Timokha (2009) that the Euler number is an important parameter when the geometry of the ambient impacting free surface generates



a gas cavity at a non-small cavitation number. Roof impact with no upper chamfer was theoretically and experimentally investigated. Compressibility associated with acoustic effects in the gas cushion is assumed secondary and neglected in the analysis. A spatially uniform compression of the gas cushion based on an adiabatic pressure-density relation is assumed. The dynamic interaction between the compression of the gas cushion and the liquid motion causes a natural frequency as previously explained. Leakage and inflow are important damping mechanisms of the oscillations (Faltinsen, 2005). Gas pocket events occur also, as already stated, for slamming in shallow liquid conditions and are affected by the ullage pressure (Lugni et al., 2010a, b).

A Bagnold-type model provides a simple mean to scale model test results of maximum pressure due to a gas pocket (Faltinsen and Timokha, 2009). Because an adiabatic pressure-density relationship is assumed, the method is questionable when condensation occurs due to overpressure during compression of the gas cavity at zero cavitation number. We are not guaranteed that it is conservative to use Froude scaling when a gas cavity occurs (Faltinsen and Timokha, 2009). The larger the model scale pressure is, the larger is the possibility of non-conservative estimates by using Froude scaling.

A possibility in scaling model tests with a gas cushion is to use a CFD method at model and full scale. However, the selected method has to be properly validated for slamming pressures. A first step would be to consider tank roof impact with a gas cushion that is in general less complicated than shallow liquid impact with a gas cushion. The tank roof impact case is numerically and experimentally investigated by Abrahamsen (2011) and Abrahamsen and Faltinsen (2011, 2012). A nonlinear BEM for the liquid is coupled with ullage gas flow before the closure of the gas cushion. High gas velocities with compressible gas flow occur at the final stages before closure. Numerical difficulties with a singular behavior occur at the closure. There are similarities with the “water hammer” problem. A spatially uniform compressibility with adiabatic conditions is assumed in the closed gas cushion. Abrahamsen and Faltinsen (2011) found based on a simplified analytical model that the decay of pressure oscillations in a closed air cavity is mainly due to a) nonlinear effects, b) heat exchange between the air inside the air pocket and the surrounding water and tank wall, c) boundary layer effects in the water.

In general, we cannot rule out the influence of the other flow parameters introduced in eq. (1). For instance, the bulk modulus of the gas and the temperature may matter. The temperature has an effect on physical constants. The mixture of gas and liquid can substantially lower the speed of sound (Wood, 1930; Faltinsen and Timokha, 2009). The consequence is a longer time scale for acoustic effects which means the tank structure can more easily react dynamically in terms of large structural stresses. However, the mixture of gas and liquid in an LNG tank is not homogeneous in space. Mixture of gas and liquid takes place in a layer of the LNG next to the ullage space. Korobkin (2006) and Iafrati and Korobkin (2006) analyzed 2D steep-wave impact on a vertical elastic wall with an aerated

layer in the impact region. The wave front of the incident wave is vertical and is wetting the vertical wall over the complete liquid depth at the initial time. The liquid is incompressible outside the aerated layer. A thin-layer approximation is used to account for the mixture between liquid and gas. The ratio D/Hz between the thickness of the aerated layer and the liquid depth Hz is assumed small. The effect of the elasticity properties of the vertical wall is accounted for by the beam equation. A case study of the maximum structural strain was presented for D/Hz = 0.01, 0.1, 0.25 as a function of the void fraction between 0 and 30%. If we disregard small-amplitude oscillatory behavior, the result with zero aeration is conservative and can be considered as a first approximation.

The time scale of a fluid dynamic phenomenon such as acoustic effects relative to natural periods of structural modes contributing to large structural stresses is important in judging if a particular fluid dynamic effect matters. If a fluid dynamic effect occurs on a time scale much shorter than important structural natural periods, the details of the fluid dynamic effect do not matter. An idea about important structural natural periods can be obtained from the numerical studies by Graczyk (2008) who examined slamming load effects on a part of the Mark III containment system. The hydrodynamic part of the analysis was strongly simplified while the structural modeling was complete. Typical main dimensions of the tank could be a length of 43m, a breadth of 37m and a height of 27m. Because the corners complicate the analysis and structural details were not available, the studied segment of the containment system was not adjacent to corners. The lateral dimensions of the panel were 3300 × 840mm. This corresponds to an assumed span of girders and stiffeners in two perpendicular directions. The thickness of the segment was approximately 300mm. The resin ropes, the steel plate and two layers of plywood with a layer of foam in between were included. These components are the most important in a dynamic analysis.

A slamming case is analyzed numerically in terms of response spectra. An average slamming pressure of 10 bar acting on the considered segment was assumed. The time duration of the loading was 3ms. The effect of added mass was included in a very simplified way. The maximum response values were of significance for the evaluation of the structural strength. Four different locations were studied. It is not only the lowest modes, governed by the steel response, that matter. There is a significant influence from modes with a range of natural frequencies from about 100 to 500Hz. An important effect of these higher modes is compression of the foam and local bending of the plywood plate adjacent to the resin ropes. The effect of liquid compressibility is believed to matter for frequencies of the order of 1000Hz and higher if the influence of bubbles in the liquid is neglected. As stated earlier, a mixture of gas and liquid can significantly lower the speed of sound and thereby increase the time scale of acoustic effects.

If the ratios between the impact duration and important natural periods are small, the fine details of the hydrodynamics are not needed in describing what the maximum structural stresses will be. Earlier we briefly described the analysis by



Faltinsen (1997) when the ratio between the impact duration and the important natural period is small. The situation for the membrane structure considered by Graczyk (2008) is different. Significant response of the lower plywood occurs already during the slamming impact, i.e. before the free vibration phase. This is both due to the slamming duration and the higher natural frequency of the lowest important mode (125-165Hz).

Maillard and Brosset (2009) presented experimental probability density functions of the rise time of the slamming pressures in their model tests with a rigid model. The rise time is defined as twice the time from the half peak value to the peak value. They related the rise time with dynamic amplification factors (DAFs) determined through Finite Element Analysis for each Limit State of the Cargo Containment System. The DAF curve was Froude scaled back to model scale in Maillard and Brosset (2009). Their results show that dynamic amplification matters. However, this procedure is approximate and not truly hydroelastic because the model tests are done with a rigid model.

The scaling of the time from model to full scale associated with slamming does not always Froude-scale. For instance, it is shown in Faltinsen and Timokha (2009) by a theoretical model of a gas cushion how the time duration of slamming pressures scales with the Froude number and the Euler number for a non-small cavitation number. Nonlinearities of the gas cushion behavior are very important at full scale but not at model scale. It may not be sufficient to represent the time history of the slamming loading by the rise time. The latter fact was discussed in connection with global wetdeck slamming where both water entry and exit forces matter.

Lugni et al. (2013a, b) have conducted model tests of hydroelastic slamming in shallow water condition by measuring pressures and structural strains. Only the highest natural period of a typical membrane structure was considered by Froude scaling. An aluminum plate was used for this purpose. The experimental set up allows for depressurized conditions so that Euler and cavitation number can be properly scaled. The fact that water and air were used raises the question how appropriate this is for LNG and NG. However, further analysis of the tests is needed to provide the effect of the many impact scenarios in shallow liquid conditions and tell how appropriate it is to use DAF based on rigid tank tests to establish structural stresses.

3.2 Error analysis of sloshing-induced slamming pressure in ship tanks

A slamming load effect analysis ought to be accompanied by an error analysis. The effect of environmental wave conditions and interactions between ship motions and sloshing must be considered. The following discussion is based on that slamming loads are estimated by model tests with forced rigid-tank oscillations obtained by numerically predicting the interaction between global sloshing loads and ship motions in specific sea states. Examples on error sources are: a) wave spectra, b) ship speed and heading, c) numerical method for global sloshing loads, d) numerical method for exterior flow (forward speed effects, roll damping), e) sloshing model test errors (bias,

precision), f) time series length in model tests (nonlinear response requires many more realizations than linear systems to obtain reliable predictions of probability density functions), g) Reynolds number effects on slamming, h) cavitation number effects on slamming, i) Euler number effects on slamming, j) acoustic effects in gas/liquid mixture, k) spatial pressure distribution, l) hydroelastic effects.

Step 1 in an error analysis is to establish all error sources and to assess the error associated with each of them. The next step is to study the propagation of errors to design pressures by, for instance, use of existing numerical tools and assume independence of error sources. Doing an error analysis is, for instance, advocated by ITTC for hydrodynamic problems. However, such an analysis for the slamming load effect associated with sloshing is not known to the author.

4 Conclusions

Slamming associated with external ship flow, green water on ship decks and sloshing in ship tanks is discussed. Both local and global external slamming problem are considered. The importance of hydroelasticity is emphasized. Hydroelasticity matters in local slamming for small local deadrise angles. Challenging benchmark tests are encouraged for numerical methods. A good example on benchmark testing is comparison with the similarity solution results presented by Zhao and Faltinsen (1993) for water entry of upright and rigid 2D semi-infinite rigid wedges at small deadrise angles.

Experimental drop results of horizontal elastic plates show no correlation between maximum slamming pressure and maximum stresses. If the time scale of a hydrodynamic effect is very small relative to the structural natural periods associated with maximum structural stress, the details of the hydrodynamic effect do not matter. When hydroelasticity does not matter and there is no gas cavity, the flow and pressure loads associated with water entry in external flow can be well approximated by potential theory of an incompressible liquid. Non-viscous flow separation may occur during water entry. Both the water entry and water exit phase matter in describing the global load effect due to wetdeck slamming on catamarans at forward speed. The water entry and exit loads can be approximated by using a von Karman method in combination with nonlinear Froude-Kriloff and restoring loads. A similar method may be used for preliminary estimates of water entry and exit loads on platform decks and subsea modules. Global slamming loads on monohulls are often simplified by using a 2D generalized Wagner model in combination with nonlinear Froude-Kriloff and restoring loads. Further development should study 3D and forward-speed effects on the slamming loads. Rules for wetdeck slamming on ships should better reflect the physics.



Slamming in prismatic ship tanks is discussed with emphasis on LNG tanks. Different impact scenarios are considered. Large filling ratios, as well as shallow and lower-intermediate depth conditions, are important. There are many contributing factors to scaling which have to be considered and one has to do certain approximations. Generally speaking, Froude scaling is expected to be a dominant effect. Correct ratio between the density of the gas and the liquid, the Euler number due to possible gas pocket effects, boiling (cavitation number), as well as hydroelastic effects, have to be considered. An implication is that the effects of viscosity (Reynolds number), surface tension (Bond number), as well as the change of the speed sound due to a mixture of gas and liquid, are secondary. Attention should be given to the accuracy of prescribed calculated tank motions used in model tests of sloshing-induced slamming.

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Prospecting experimental data of VIV to estimate dynamic behavior of a subsea pipeline with free span

Celso K. Morooka and Raphael I. TsukadaDep. of Petroleum Eng. & Offshore Petroleum Systems and Risers (LabRiser)Faculty of Mechanical Engineering & Center for Petroleum StudiesUniversity of Campinas - UNICAMP - Campinas-SP, BrazilE-mail: [email protected]


AbstractSubsea pipeline is used to link an offshore petroleum field facility at the open sea and a petroleum terminal nearby the coast, usually to export oil or gas production. In the pipeline way though the sea bottom, free spans for the pipeline happens due to irregularities of the ocean ground. In free span portions of the pipeline length, the sea current results in forces on the pipe, such as the drag and the vortex-induced vibration forces, respectively. Those forces have great influence in the pipe structural stresses and fatigue damage. Therefore, they must be carefully analyzed and considered in the pipeline design. The present work presents a study from a search of experimental data from the literature allied with experiment carried out and semi-empirical VIV approach under development. A numerical simulation procedure is introduced to predict dynamic response of a pipeline with free span. Calculations were carried out in time domain by using finite element approach.

Keywords Subsea pipeline; sea current; offshore riser; vortex induced vibration; ocean waves; offshore petroleum.

1 IntroductionGreat advancements have been achieved from the effort regarding studies about Vortex Induced Vibration (VIV) around a cylinder with circular cross section, and they are very well documented in the literature. From the other hand, most of the computational tools for numerical simulation of riser and pipeline behavior are based on empirical approaches. They are based on the two dimensional flow behavior around stretch pipes. Discrepancies between estimated and observed results in the VIV prediction through those models come fundamentally from the lack of knowledge in the mechanism of vortex generation, the formation of vortex wake and how those flow phenomena interacts with the pipeline or riser structure dynamic behavior.

Risers, and further, subsea pipelines with free spans due to uneven seabed suffer vibrations due to vortex shedding if a sea current is present. In this case, fatigue damage of the riser or pipeline will increase. Therefore, a clear understanding of the riser or pipeline behavior due to VIV is fundamental to ensure safe operation for a lifetime period estimated from the design process.

Several approaches to estimate VIV forces are outcome from studies in the literature (Williamson and Govardhan, 2004). Estimation procedures typically follow semi-empirical and numerical approaches. Each procedure presents particular restriction which introduces different kind of limitation according to the assumptions.

In previous works by the research group (Morooka et al, 2003, Morooka et al, 2007, Morooka and Tsukada, 2011) advances in the time domain semi-empirical model approach to predict the dynamic behavior of pipeline and risers due to VIV have been demonstrated, and depicted the complexity and limitations of VIV predictions for risers and free span portion of a subsea pipeline. Time domain


procedure has been used which has the advantage to represent nonlinearities from the structure and boundary conditions. And, also experiments have been carried out. The semi-empirical approach presents simplicity for computation; however, it requires great effort to take into account the complexity of influence of the pipe movement into VIV force mechanism.

In the present paper, the semi-empirical approach to estimate VIV force for subsea pipelines will be presented. Pipeline behavior will be numerically simulated and discussions will be carried out.

Nonlinear Finite Element Method (FEM) is applied and, for the simplicity, effects of in-line VIV are neglected. Further, two-dimensional fluid flow is assumed around the pipeline transverse section. For each pipe segment the VIV forces are calculated based on experimental data (Vikestad, 1998, Blevins, 2009). Then, the results are obtained by numerical integration in time domain. Finally, comparisons with a pipeline model experiment (Cunha et al, 2009) are carried out, in order to verify accuracy of the present numerical approach.

Fig. 1 Flowchart of the procedure to calculate the VIV forces.

2 Prospecting experimental data for VIV forces

Pipeline is taken divided into segments (or elements) of equal size, and the lift coefficient (CL), vibration frequency (f) and phase angle between the VIV force and motion (φ) are obtained for each pipe segment (“strip”). The VIV force on each segment can be calculated from Eq. 1.

(1)

where, L is the length of the pipe segment.

The main challenge of semi-empirical methods is to determine CL, f and φ which are function of the pipe movement. In previous works, f has been considered equal to the vortex shedding frequency in a rigid and stationary cylinder. This frequency is calculated from the Strouhal number (St = fxDo/U). CL is obtained from experiment with rigid and stationary cylinder. And, Morison’s equation is applied for representing the viscous and inertial effect, respectively, due to the pipe motion.

This approach is suitable for conditions with ocean waves and prescribed pipe motions. From the other hand, vortex shedding behavior and VIV mechanism are nonlinear due to effects of the pipe structure motions. Superposition of forces from a stationary cylinder and from a cylinder oscillating in water, no longer should represent the VIV problem with accuracy. Possibly, influences in the VIV force such as those coming from changes in the vortex shedding pattern (Williamson and Roshko, 1983) should not be very well represented in the previous approach (Morooka and Tsukada, 2011).

Time domain approaches, as in previous work, are important and meaningful to evaluate structural non-linearities, soil effects and traveling waves in riser and pipeline behavior. In the present work, the procedure as described through Fig. 1 is followed as the one another step to improve the VIV prediction and to make the result more accurate.

2.1 Estimation of pipe segment vibration frequency (f)

Added mass in VIV phenomena has been described through several experiments in the literature (Vikestad, 1988; Sarpkaya, 1978; Gopalkrishnan, 1993). In those, evidences have being observed that the pipe vibration frequency is approximately equal to its ‘true’ natural frequency, i.e., the natural frequency calculated with changes of added mass due to VIV. Thereby, pipe vibration frequency (f) can be calculated based on experimental data of the variation of Ca with VR.

By following the flowchart as presented in Fig. 1, the first step is to calculate the pipe natural frequency in still water condition. In the present experiment (Cunha et al, 2009), the pipeline responded for the cross flow VIV, in the first mode frequency, for all the range of current velocities considered in the experiment. Therefore, only this mode frequency has been considered in the analysis and numerical simulations. Added mass coefficient equal to 1.0 was considered for computations. Comparison of the first mode natural frequency in the cross-flow direction from decay tests in the experiment (fn,exp= 1.025) and from numerical simulations (fn,calc = 1.026) has shown a small deviation of around 0.1% which shows good accuracy of pipeline mass and stiffness estimated for calculations. More details of numerical simulation are given in further description.

Prospecting experimental data of VIV to estimate dynamic behavior of a subsea pipeline with free spanCelso K. Morooka and Raphael I. Tsukada


Fig. 2 Added mass coefficient (Ca) with reduced velocity (VR) from Vikestad (1998) experiment.

Natural frequency of pipeline vibration in still water is used to calculate the Reduced Velocity (VR=U/fn x Do). And, the added mass coefficient (Ca) is determined from the linear interpolation in VR, from the experimental data presented by Vikestad (1998) for elastic mounted rigid cylinder, as in Fig. 2, in Re number ranging from 14,000 to 65,500. The cylinder is restrained to move only in the cross-flow direction, and end-plates are fit at the both cylinder ends. The mass ratio is 1.306 (without the added mass) and the damping ratio is around 0.1% (in air). The maximum vibration amplitude is ACF / Do ≈ 1.15 and it is found for VR ≈ 6.0. Vikestad (1998) observed a good agreement of added mass coefficients for an oscillating rigid cylinder obtained from experiment, when compared with the other ones (Sarpkaya, 1978; Gopalkrishnan, 1993). Finally, with the Ca, the ‘true’ natural frequency is calculated by performing the Eigenvalue analysis with the added-mass matrix [Ma] updated.

Fig. 3 An overview of the (a) In phase force coefficient (Cmv), and (b) Out of phase force coefficient (Cdv), obtained from Blevins (2009).

3 Estimation of lift coefficient (CL) and phase angle (φ)

In the present approach, CL and φ are, respectively, determined from the experimental result presented by Blevins (2009), for a rigid vertical cylinder. The experiment intended to reproduce an ideal two-dimensional spring-supported rigid cylinder that displaces perpendicularly to its longitudinal axis. The cylinder length is approximately 1.1 meters and the mass ratio is near to five (added mass included). The vibration amplitude and frequency were measured for the flow velocity ranging from 0.15 m/s to 0.92 m/s for steps of 0.01 m/s, corresponding to 2 < VR < 12 and 10,000 < Re < 80,000. For each flow velocity, the structural (magnetic) damping factor has been adjusted between 0.002 and 0.4, in order to achieve target amplitudes (ACF/Do) between 0.05 and 1.45 with 0.1 steps. Measured force was decomposed into in phase (Cmv) and out of phase (Cdv) force coefficient components, in relation to the cylinder movement. The force coefficient for non-excited cases (Cdv > 0) was achieved by decay tests, by using similar cylinder. The cylinder was displaced in the cross-flow direction and released in water, with flow velocity as already mentioned.

Fig. 4: (a) CL and (b) φ with ACF/Do and StU/fD.

Tables of Cmv and Cdv, respectively, as function of ACF/Do and StU/fD were reproduced from Blevins (2009). In Fig. 3, an overview of the tendency of those results can be observed. For the present study, intermediate values have been bi-harmonically interpolated, as also in Blevins (2009). Negative values of Cdv are observed for 1 ≤ StU/fD < 1.6, as in Figure 3a. It means that in this region the fluid is providing energy to the pipe and lock-in happens. It occurs for vibration frequencies



between 70% and 100% of the natural vortex shedding frequency. As the amplitude of vibration increases, Cdv becomes positive and damping is created, and the maximum amplitude of VIV is limited. Comparisons for Cdv have been carried out between oscillating rigid cylinders results (Blevins, 2009; Sarpkaya, 1978; Gopalkrishnan, 1993). In Fig. 3b, signal change from positive to negative happens for Cmv at StU/fD ≈ 1. This variation is similar to that observed in the Ca x VR curve (Fig. 2), where the change occurs around VR ≈ 7. StU/fD ratio can be understood as the ratio between the natural frequency of vortex shedding and f. Thereby, when the natural frequency of vortex shedding becomes equal to f, signal inversion happens for Cmv.

Figures 4a and 4b present CL and φ against ACF / Do and StU/fD, respectively. Results for oscillating horizontal rigid cylinder experiments in Staubli (1983) show similar trends for CL and φ, respectively. From Fig. 4a, CL increases with ACF / Do and the maximum values happen for StU/fD < 1. Thus, as larger is the CL bigger is the amplitude of vibration, for f larger than the natural frequency of vortex shedding. It agrees with the high values of Cdv found at this region (Fig. 3a). In Fig. 4b, signal inversion can be observed for φ. It is a consequence of the quick decrease of Cmv when f approaches to the natural frequency of vortex shedding (Fig. 3b). Experiments in Williamson and Rosko (1983) have shown that in lock-in condition, this jump for φ happens, and it could be related to the change of the vortex shedding pattern.

Once Cmv and Cdv are known, CL and φ can be calculated by the following equations.

(2)

(3)

4 Subsea pipeline behavior

The description of pipeline displacements combines the total and the updated Lagrangian formulation, and the Finite Element Method (FEM) is used to model the pipeline behavior. Geometrical nonlinearities, three-dimensional description, and large displacements and rotations with small deformations are taken into account in numerical simulations of the pipeline structure behavior. In the present study, formulations and the computer algorithm as presented in Mourelle et al (1995) are applied.

4.1 Dynamic Behavior of the Pipeline

For the dynamic analysis through time domain integration, the following differential equation (Eq. 4) for pipeline

behavior is considered.

(4)

where, [Ke] is the stiffness due to the elastic behavior of the material, [Kg] is the geometric stiffness matrix of the pipe, [Ms] is the structural mass matrix, and [Ma] is the added mass matrix. The structural damping matrix [B] is evaluated by the Rayleigh damping. Due to the non-linear dependency of the geometric stiffness matrix with the pipe displacement {x}, the stiffness matrix is updated at each time step of integration. Finally, the solution of the dynamic analysis is obtained after solution of the static analysis of the pipeline.

4.2 Eigenvalue analysis

From the free-vibration analysis the natural vibration mode shapes ([X]) and frequencies ({ω}) are obtained, as follows:

(5)

5 Results and analysis

Experiment with a pipeline model was conducted at the IPT towing tank facility (Cunha et al, 2009). The pipeline model positioned horizontally throughout the tank width of 6 meters, and towed along length of 220 meters of the water tank with 4 meters depth, in calm water. Figure 5 shows a scheme of the experiment set-up. The Aluminum pipe is attached to the moving carriage by universal joints at the both ends. In one of the pipe ends, a small gap was left to avoid increase of the tension due to pipe self-weight and current drag. End plates were installed in both ends of the pipe in order to avoid three dimensional effects of the flow. Uniform current has been reproduced by advancing the carriage with a constant towing speed.

Fig.5 Set-up of the pipeline model experiment.



Table 1 Pipeline model main characteristics (Cunha et al, 2009).

Table 1 summarizes main characteristics of the pipeline model. Tests have been carried out for Reduced Velocities (VR) ranging from 1 to 10, and Re number from 430 to 3500.

Decay tests were carried out for the pipeline model, respectively, in air and in water conditions. The pipe aspect ratio (L/Do) is approximately 230, and the pipe mass ratio (without the added mass) is nearby 1.0. The natural frequency in air is about 2.36 Hz, with a structural damping ratio of almost 0.9%. In water, the natural frequency diminishes to 1.03 Hz, and the damping ratio increases to 6.35%, as it is already expected due to hydrodynamics effects. Added mass coefficient has been estimated from decay tests, and it is about 1.0. By these parameters, a low mass-damping parameter (≈0.02) is found. Then, the VIV response of the pipeline in the experiment should occur in a different pattern if compared with results for high mass ratio experiment (Blevins, 1990).

Strain gauges were attached into the outer surface of the pipeline model, and bi-directional accelerometers were installed inside the pipe to obtain motions for in-line and cross-flow directions, respectively. Coating was carefully applied for sealing and smoothing the region around strain gauges to minimize interference into the global response of the pipe. Load cells for in-line and the cross-flow directions, respectively, were also assembled at both ends of the pipeline.

For numerical simulations, the pipeline model is divided into 200 elements with constant length, and a time step of 0.01 seconds was considered. Pinned boundary conditions are taken to represent universal joints at each pipeline’s end. Movement of the pipe end which is axially free to

move was observed in all numerical simulations, and a maximum displacement of 1.6 mm was obtained which can be considered as very small if compared with the gap left for this pipe end (Fig. 5).

Fig.6 Comparison of (a) the maximum cross-flow vibration amplitude, and (b) vibration frequency, in the middle length of the pipeline, from experiment (Cunha et al, 2009) and numerical simulation.

Comparisons for the maximum vibration amplitude and frequency, experiment and simulations, are presented in Figure 6a and 6b, respectively. The VIV for the cross-flow direction is the main objective in present study, therefore, VR > 4.0 condition is focused in the analysis. And, it is suited for a Re number ranging from 1,700 to 3,500. Experiment has shown an important influence of the in-line VIV for low VR cases, in which the present numerical procedure cannot represent.

The Strouhal number (St) is found through empirical equation for an “infinitely” long, rigid, smooth and unconfined cylinder, in an uniform incoming cross-flow, i.e., flow around a non-vibrating cylinder with negligible effects of surface roughness, with a large enough aspect ratio and free-stream turbulence (Norberg, 2003). For the range of Re number in the present study, St is around 0.21. And, this Strouhal number was used to find CL, φ, and to determine the natural vortex shedding frequency indicated by the solid line, in the Fig. 6b. φ is assumed constant along the pipeline length based on the uniformity of the current profile and the use of end-plates in the experiment.



Fig. 7 Time history from experiment for the cross-flow displacement, measured at the center of the pipeline length, for different reduced velocities.

In Fig. 6a, black marks represent the measured amplitudes of vibration from experiment, and the numerical simulation results by the dashed line. Good agreement is observed between experiment and numerical simulation results. With the exception in the region of VR located between 6 and 7 in which, vibration amplitudes achieve the maximum. The observed difference could be related to the restriction imposed to cylinder end movements in the experiment.

Hydrodynamic coefficients from the experiment with a rigid tube constrained to move only into the cross-flow direction were used to obtain f, CL and φ. Moe and Wu (1990) and Jauvtis and Williamson (2004) conducted experiment with rigid cylinder with low mass ratio and two degree of freedom, which means the cylinder is enabled to move into the in-line and cross-flow directions, respectively. From those, it is possible to observe evidences of the increase of peak amplitude of

vibrations and a shift of those peaks for larger VR, if compared with the result from the others experiment with different mass ratio for the cylinder. However, in the present study, experimental results with a cylinder restrained to move only into the cross-flow direction, such as that presented by Vikestad (1998) and Blevins (2009) are used to determine hydrodynamic coefficients for the numerical simulations.

Fig.8 Time history from numerical simulations for the cross-flow displacement, computed at the center of the pipeline length, for different reduced velocities.

In the experiment with a pipeline model at the towing tank (Cunha et al, 2009), the pipe can be considered as a flexible pipe with low mass ratio. Results from that experiment are used to verify accuracy of the present numerical simulation approach. The main difference of that experiment with the Moe and Wu (1990) and the Jauvtis and Williamson (2004) ones is the flexibility of the pipe model. Then, vibration amplitudes are different along the pipeline length according to the excited mode shape. Since VIV force magnitude depends on vibration



cases with small vibration amplitude (ACF/Do), the distribution of VIV forces along the pipeline length is almost uniform with small decrease nearby the pipeline ends. However, for cases with large amplitude, VIV forces present significant variations along the pipeline length with a decrease around the middle of the pipe, where the peak amplitude of vibration occurs.

As in the present work, the VIV phenomenon is related to the number of degrees of freedom allowed for the cylinder displacements, i.e., only the cross-flow motion, or both simultaneous the in-line and the cross-flow motions. Degree of freedom of the cylinder among others has a huge influence in defining the vortex shedding process as well as the magnitude of hydrodynamic forces involved. Then, due to the complexity of VIV forces and the variety of possible configurations to be addressed for risers and subsea pipelines system design, large amount of costly experiment is needed in order to build an optimal hydrodynamic coefficient database. Therefore, a further alternative besides the experiment could be the Computational Fluid Dynamics (CFD) which appears as a powerful tool to describe the hydrodynamics of the VIV. Recently, very promising CFD simulation results for two dimensional flow around a cylinder section have been shown in the literature (Saltara et al., 2003, Menter et al., 2006, Wanderley et al., 2008), among others, in which, good agreement are observed with experimental results.

6 Conclusions

In the present study, a consistent and sistematic survey of data from experiments have been carried out in the literature. A careful and detailed analysis was conducted and allied with comparisons made with experimental results from the towing tank with a pipeline model, an improvement of the semi-empirical approach to predict VIV force in a subsea pipeline with free span, from the previous development, is described.

Calculation of VIV forces based on hydrodynamic coefficients achieved from oscillating rigid cylinders in uniform flow is presented. Advancements from previous works are demonstrated by comparisons of numerical simulation results with experimental ones and, in general, a good agreement was observed. Further investigation is still demanded, particularly, for the VR ranging from 6 to 7, around the peak amplitude region, where numerical simulation still underestimate the response amplitude of vibration of the pipeline, and the frequency of vibration is overestimated.

Finally, a continuing effort through developments of numerical procedure and experiments are still needed to clarify and to get a good estimation of VIV hydrodynamic forces, to make the design process of service lifetime of subsea pipelines more and more reliable.

amplitude, it is expected that this force also changes along the pipeline length as can be observed in Fig. 9.

Furthermore, a flexible pipe has several modes shapes and depending on the current velocity, it is expected to vibrate in different mode shapes. Analysis of experimental results has shown that only the first mode of vibration occurs for the cross-flow direction. Although differences pointed in above, effects as observed by Moe and Wu (1990) and Jauvtis and Williamson (2004) are expected in the experiment with pipeline model in the towing tank, and this fact could explain differences in comparison in Fig. 6a and 6b.

Fig.9 Time varying VIV force distribution along the pipeline length for different VR from numerical simulations.

The present approach to estimate the pipeline response shows some advancement in comparison with previous ones (Morooka et al, 2007; Morooka and Tsukada, 2011). By considering the ‘true’ natural frequency for f instead of simply the natural vortex shedding frequency, better numerical simulation results are obtained, as in Fig. 6b. Furthermore, by following the present procedure larger set of CL data were able to apply.

In Fig. 7 and 8, time series for the cross-flow displacement at the middle length of the pipeline, measured from experiment and from numerical simulations, are shown for VR = 4.68, 5.71, 6.29, 6.68, 7.41 and 8.59, respectively. In those cases, maximum amplitude of vibration were observed, and for all cases analyzed, stable vibration behavior was observed, and the frequency followed as observed in Fig. 6b.

Figure 9 shows the computed distribution of VIV forces along the pipeline length for different VR. The forces are presented in a dimensionless form (CL = FL/(0.5 ρ U2 D)). It is observed that for



Acknowledgement

The authors would like to acknowledge Petrobras, Finep, PRH-ANP, CNPq, Capes and Fapesp for the continuous support for the research.

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Abstract

DP Systems are based on control, filtering and optimization solid theoretical background, and the technology related to sensors, actuation and computational systems are consolidated and reliable. Therefore, the offshore operations are increasingly supported by DP Systems since the 70’s. However, there are still space for new developments and innovative solutions to improve DP performance and to be applied to more complex offshore operations. This paper presents four research topics conducted by the Brazilian Universities and Petrobras related to the improvement of the DP Systems.

Keywords

Dynamic Positioning, Sliding Mode, Weathervane, Cooperative Control, Wave basin, Simulator.

1 Introduction

The University of São Paulo (USP) in cooperation with Petrobras conduct R&D projects related to DP Systems, aiming to improve such systems and to adequate them to new offshore operations and conditions. This paper presents a brief description of four R&D projects:

l Cooperative control techniques applies to multi-vessel DP operations

l New approach for weathervane control

l Application of non-linear sliding mode control to DP systems

l Thrust allocation algorithm considering the thruster interference effects

2 Cooperative control techniques applied in multi-vessel DP operations

With the increasing of ultra-deep water oil exploration activities, the utilization of complex undersea structures and equipments are becoming more common and economically advantageous. Since they are normally large and requires a fine positioning in the sea floor, the installation normally requires multi-vessels operations. Those operations need a high level of planning and coordination. An example that involves the operation of two ships was studied by Fujarra et al. (2008). All multi-vessels operations are cases where cooperative control could be applied.

New developments on DP systems

Eduardo Aoun TannuriNumerical Offshore Tank, University of São Paulo (TPN-USP) São Paulo, SP, Brazil [email protected]



New developments on DP systems Eduardo Aoun Tannuri

In the Oil and Gas industry, there are many other cases where cooperative control could be applied. In Queiroz et al. (2012) an oil transfer operation was studied. Two shuttle tankers had to maintain their relative position while oil was transferred between them, in order to avoid the necessity of shore terminals. A fully numerical time domain simulation was carried on and the results showed the benefits of the cooperative control, when compared to the non-cooperative one.

Back to sub-sea equipment installation and undersea structures launch operations, it is important to coordinate the relative movement between the ships in order to properly place the equipment or structure at the sea bottom. This case was tested here with a conceptual experiment. Two small-scale offshore tugboats models are used for the tests. Both of them are equipped with two main thrusters at the ship’s stern, two tunnel thrusters, one in the bow and one in the stern. All tests are carried out at the TPN’s wave tank. In this work, the consensus control concepts are applied, following Ren et al. (2007). The advantage of the cooperative control is demonstrated, with more accurate control of the relative positioning during station keeping or transient maneuvers. A more comprehensive discussion about the present research topic can be found in Queiroz and Tannuri (2013). 2.1 Experimental set-up description

The experiments were conducted at the USP academic tank in order to validate the controller under various environmental conditions. The experiments used two 1:42 reduced scale model of a typical offshore tugboat, with the full scale properties indicated at Table 1.

Table 1 Model and Full Scale tug boat properties.

The lightship condition was used in the tests. The vessels are equipped with two main thrusters, two tunnel thrusters one in the bow and one in the stern, and an azimuth thruster which is not going to be considered in this experiment (Fig 1). The tank has a set of fans and a wave generator that produces wind and waves parallel to the tank (Fig 2). A Qualisys measuring system is used for obtaining the horizontal position of both vessels, and the control loop is performed at the scan rate of 100ms.

Fig. 1 DP Model (upside down) and thrusters information.

Fig. 2 Models under environmental loadings due to fans aligned with the tank length.

2.2 System and controllers description

The Dynamic Positioning (DP) System is only concerned about the horizontal motions of the vessel, that is, surge, sway and yaw. The motions of the vessels are expressed in two separate coordinate systems (Fig 3): one is the inertial system fixed to the Earth, OXYZ; and the other, or , are the vessel-fixed non-inertial reference frames. The origin for this system is the intersection of the mid-ship section with the ship’s longitudinal plane of symmetry. The axes for this system coincide with the principal axes of inertia of the vessel with respect to the origin. The motions along of the local axes are called surge, sway e yaw, respectively.

Fig. 3 Coordinate systems.

The adopted DP controller consists of a regular PID for each degree of freedom for the non-cooperative control. Equations (1) and (2) show the controller for vessel A and B respectively:



(1)

(2)

with i=1,2,6 representing each controlled degree of freedom. The upper index NC represents the non-cooperative controller part, A and B represents each vessel, xdes is the desired value for each degree of freedom (set-point), KP is the proportional gain, KD is the derivative gain and KI is the integral gain. The adopted values for KP, KD and KI are the same for both vessels.

A simple thrust allocation logic is used in the present work, since there is an algebraic relation between the total forces and the thrusters commands, supposing that both main thrusters are equally commanded. No wave filter is considered.

All PID gains were empirically adjusted, and Table 2 shows the obtained values. Both vessel controllers are adjusted with the same gains.

Table 2 KP, KD and KI control gains.

For the cooperative control the same controller is used with an additional term proportional to the relative distance of the vessels. Equations (3) and (4) show the controller of vessel A and B for the cooperative control:

(3)

(4)

where KCxi is the cooperative control gain. This formulation is

based on the consensus control defined by Ren et al. (2007). The cooperation part of the controller can be considered as a “virtual spring” connecting both vessels. Fig 4 shows the block diagram of the cooperative controller. It is considered that an efficient data transmission system is available, since the position and heading information of each vessel is transmitted to the other with negligible delay.

It must be noticed that the “virtual spring” term will introduce a new natural period in the system, that creates a potential resonance for low-frequency motions. An analytical or numerical frequency domain analysis of the multiple resonant frequencies and how they influence the DP system performance must be done. This can be used for adjusting the value of the cooperative control gain. This will be done in a next step of the research, and in the present paper, only the experimental verification was done.

In order to demonstrate the benefits of the cooperative control, due to physical limitations of the tank, only the sway and yaw movements are considered for the cooperative control design. The surge movement of each vessel is independently controlled (KCx1

= 0).

Fig. 4 Cooperative DP system applied to the relative position and heading control.

2.3 Experimental result

Several experiments demonstrated the effectiveness of the proposed controller, and one of them will be detailed in this section. The vessels are kept at a distance of 0.9m, parallel to each other. A 0.2m step set-point change is then imposed to the lateral position followed by a 30 degrees step set-point change in the yaw angle. Non cooperative control (KCx2

= 0; KCx6

= 0) was initially considered and then the cooperative control was turned on with (KCx2

= 10; KCx6= 15). Fig 5 shows

the layout used in the experiments. Wind and wave actions were considered during these experiments. The wind speed is roughly adjusted to 4m/s (25m/s in full scale). The wave height is approximately 0.1m (4.2m full scale) and 1s period (6.5s full scale).

Fig 6 shows the Y position and the yaw angle of both vessels. As it can be noticed when the cooperative control is turned off (from 240s until 390s), both position curves (Y and yaw) get apart from each other. In fact, Fig 7 shows the relative distance between midship, bow and stern points. At 240s when the cooperative control is turned off the relative distances errors get significantly higher.

Fig. 5 Maneuvers in sway and yaw with environmental action.


Fig 6 Vessel A and B Sway position and Yaw angle with environmental action.

Fig 7 Relative distance from Keel mid ship, bow and stern between the vessels for cooperative and non-cooperative control.

The midship relative distance mean error calculated for the cooperative and the non-cooperative control are respectively 2.41×10-2m and 7.17×10-2m. An improvement of approximately 3 times is verified using the cooperative control with the same level of power consumption.

Of course, the practical implementation of this controller requires a reliable and fast data exchange system between the DP system of both vessels. The robustness of the proposed controller considering data exchange failure is being investigated.

3 New approach for weathervane control

Modern DP Systems presents the “weathervane mode”, in which the vessel automatically reaches the best heading angle, still maintaining the position of the vessel reference point.

This mode can be applied in operations that do not require a strict definition of the heading angle, such as drilling and offloading. The common approach for the weathervane mode is based on the control of the forward end of the vessel (Pinkster and Nienhuis, 1986; Davison et al., 1987). In that case, heading is not effectively controlled, and the vessel naturally searches the weathervane angle (analog to a “flag”).

One drawback of this strategy is that it only works for reference control points close to the bow of the vessel. Furthermore, sometimes it is necessary to impose limiting values to the heading angle, due to the proximity of a platform, for example. In that case, when the free-heading reaches the limit, this strategy must then be switched to a conventional 3-axis control. A broad discussion about the drawbacks of a simple free-heading weathervane control for offloading tandem operation was presented by Bravin and Tannuri (2004). In that paper, the authors alternatively proposed a controller that automatically switches to a 3-axis control when the vessel heading is larger than a limiting value. That strategy is based on a variable-gain angle control. This introduces non-linearities in the control system and increases the number of parameters to be adjusted.

Fossen and Strand (2001) developed a controller using the same principle proposed by Pinkster (1986), eliminating the first drawback of the previous controller, since it could control the midship positioning. The idea of the WOPC (Weather Optimal Position Control) is to update the set-point position for the bow-reference, in order to keep the mid-ship in a stationary position. This technology is proprietary, in the name of ABB Industry. A new approach to estimate the weathervane angle is being developed and tested. It requires no information about the environmental condition, eliminating all the drawbacks of the approaches previously mentioned. The proposed method is based on Zero Power Control (ZPC) techniques (Morishita et al., 1989) used to minimize the control action of a closed loop system. This methodology (named as ZPC-W) is very general, allowing the vessel to weathervane while controlling positioning for any reference point. Furthermore, heading angle is in fact controlled, and the set-point is constantly changing, searching for the weathervane angle. So, any limitation necessary to be imposed to the heading angle can be simply included in the definition of the set-point and time changing weather is not a limitation.

The method was implemented in the Numerical Offshore Tank 6-DOF non-linear dynamic simulator, and several numerical tests indicated its effectiveness. A comprehensive set of experimental tests in model scale also confirmed the good performance of the proposed method.

The diagram of the proposed controller is presented in the Fig 8, where the sway and yaw controllers are shown. The yaw set-point adaptation law is indicated by the red path in the diagram. It must be stressed that different types of controllers can be used, and in this paper, an uncoupled PD controller is applied for each DOF. As can be verified, the implementation



of the ZPC-W in a real DP System is quite straightforward, since it does not require any deep modification in the structure of the control and filtering algorithms.

The vessel heading set point is constantly adapted, using the following adaptation law:

(5)

where: Ψ ̇_SP: Vessel heading set-point time-derivate K: Adaptation gain F_DP^y: DP controller sway force

Fig. 8 Block Diagram for the proposed ZPC-W.

Fig 9 shows the performance of the system for a current only incidence. The heading set point is automatically updated to seek the angle in which the total sway force is zero. Miyazaki and Tannuri (2013) demonstrated that this heading is shown to be very close to the optimal (minimum consumption). Also, this solution is shown to be stable for a defined range of the adaptation gain.

Fig. 9 Application of the ZPC-W for a current only incidence.

3.1 Numerical simulation results

The ZPC-W was implemented in the time-domain simulator of the TPN (Numerical Offshore Tank – USP). The simulator considers the 6-degrees of freedom of the body and non linear effects and dynamic effects, such as wave forces.

The first set of tests considered a typical DP-barge, with the main properties indicated in Table 3. The Barge DP layout is shown in Fig 10, and consists of three fore-body azimuth units and three stern ones. The maximum thrust of each unit is 220kN.

In all simulations, from t = 0s to t = 2000s, the heading set point is fixed (headed to East). From t = 2000s onwards, ZPC-W is then turned on and the heading set point was adjusted following the adaptation law defined in the equation (8).

Table 3 Typical barge properties.

Fig. 10 Barge thrusters layout.

Fig 11 illustrates a quite common environmental condition in Brazilian offshore oil fields. In that figure, it is also presented the trace plot of the vessel and the time series of position, heading and total DP sway force. As can be verified, the vessel final yaw angle is approximately 60o, corresponding to a position with null sway DP force, as expected. The motion of the midship point (PosX and PosY plots) is acceptable during the heading change. More simulation results can be found in Miyazaki and Tannuri (2012).

Fig. 11 ZPC-W for a DP-Barge, midship control point, Brazilian typical environmental condition.



3.2 Experimental results

Several experiments were conducted at the USP academic tank. The experiments used a 1:125 reduced model of a typical Suezmax tanker in ballasted condition, with the properties shown in Table 4 (full scale values). The vessel is equipped with a main propeller and two auxiliary thrusters, namely bow and stern thrusters (Fig 12).

Table 4 - Main properties of the tanker.

Fig. 12 DP Model and Thrusters information.

The tank has a set of fans that produces wind parallel to the tank. For all experiments, a conventional 3-axis DP System is used in the initial phase of the test, with -45ºyaw set-point (position indicated in Fig 13). After some time, the ZPC-W is then turned on to search for the weathervane angle, aligned with the incoming wind direction.

Fig. 13 Test set-up and initial vessel position.

Fig 14 shows the experimental results of tests considering two different control point positions. For all tests, the only environmental agent is the wind, and it comes from the Positive Y direction (as indicated). As can be verified, the ZPC-W could automatically take the vessel heading to the desired heading for all cases. The motion of the control point is also indicated in the figures (red line). Fig 15 shows the summation of the squared thrusts. This value can be roughly considered as proportional to the total DP Power. The red line indicates the filtered value, since the thrust high frequency oscillations are even amplified by the square operation. For all cases the DP power is reduced when the vessel reached the weathervane angle, as expected.

The results so far showed that the W-ZPC is able to align the vessel with the environmental force, thus minimizing DP system requirements. This fact can be stated by sway control forces decrease. The implementation of the proposed controller is quite straightforward, since it is based on a simple correction on the heading set-point based on the total sway DP force. One of the main advantages of this controller is that the reference point does not need to be at the vessel bow, as required by traditional weathervane controllers.

Fig. 14 Experimental results for different control points (Vessel position).



Fig. 15 Experimental results for different control points (DP Power Estimate).

4 Application of non-linear sliding mode control to DP systems

Commercially, DP Systems are based on an Extended Kalman Filter (EKF) and conventional controllers (Proportional Derivative, PD). Integral action is provided by the compensation of estimated low-frequency external forces. The estimation of such forces is performed by the EKF. This control architecture was first proposed by Balchen et al. (1976). Several other researchers have improved the original controller proposed by Balchen (for example, Saelid et al., 1983; Grimble et al., 1980; Fung and Grimble, 1983) and it is still nowadays the basis of the commercial DP Systems.

However, there are some problems related to the application of a linear PD controller to the DP Systems. Gain adjustment is a very complicated task which requires time-consuming tests at sea during the DP commissioning. Moreover, the controller’s performance varies with the environmental and loading conditions, which is not desirable as some DP operations take up to 30 hours, for example offloading

operations. The DP operator must manually alter the controller gains according to the environmental conditions. Furthermore, internal automatic gain scheduling is used to adjust the control gains when the loading condition of the vessel changes. Finally, the nonlinearity of the model, related to the heading angle, demands adjustments of the control parameters for different angles (normally in steps of 15°).

Another important issue is the robustness of the controller. The mathematical model used to describe the vessel’s motion at sea, where the vessel is subjected to wind, currents, and waves, is highly nonlinear, and some phenomena are difficult to model mathematically. Thus, the DP control’s design must consider the property of robustness. Performance and stability must be guaranteed for dynamic models, similar to (but not the same as) those of the nominal model used for the controller’s design. Robustness issues were initially considered using a linear approach in DP design in the 1990s. Several authors, including Katebi, Grimble and Zhang (1997), Nakamura and Kajiwara (1997), Tannuri and Donha (2000), and Donha and Tannuri (2001), applied the H∞ methodology. The controller presented satisfactory robustness properties, with good performance in the presence of large variations in environmental conditions, modeling errors, and parameter uncertainty. However, it is a linear controller, which is based on a linear model of the system. Thus, different controllers must be designed with several points defined in the state space that are close to points that the vessel reaches during operation. A “gain-scheduling” approach should then be used (Yoerger; Newman and Slotine, 1986). Nguyen and Sørensen (2009) proposed a hybrid DP system with supervisory switching control logic to alternate between the bank of controllers and observers. Unlike a conventional gain-scheduling approach, there are structural differences among the controllers, and different control logics can be used for a range of calm to harsh environmental conditions. The authors demonstrated the stability of the system and presented an experimental validation.

Nonlinear controllers have been applied to DPS to overcome linearization problems as they do not require switching controllers. Fossen and Strand (1998), Fossen and Grovlen (1998), Aarset et al. (1998), and Zakartchouk Jr. and Morishita (2009) applied nonlinear back stepping controllers with very good results. Some difficulties in the parameters tuning were also verified. Nonlinear control theory has also been applied to other problems related to vessel motion control, such as rudder-roll stabilization (O’Brien, 2009).

Tannuri et al . (2010) proposed the application of nonlinear sliding mode control (SMC) for DP design. The SMC is an approach suitable for nonlinear systems when there is a high level of uncertainty pervading the model, originally developed by Utkin (1978). The SMC is accurate, insensitive to external disturbances and simple



to implement and tuning. However, the main disadvantage of this technique is the effect of control action high frequency oscillations, called chattering. The complete n-th order system control problem is reduced to a first-order problem, which is optimally solved by an on-off control, which causes the chattering. This undesirable effect can be reduced (or eliminated) by changing the dynamics around the sliding surface, ie, introducing a boundary layer as suggested by Slotine ; Li (1996). The controller guarantees the good performance under a large range of environmental conditions, without degradation in severe conditions and for loading variations. The performance of the controller was evaluated through tests with a scale model of a tanker. Recently, a new control method was being applied to avoid the chat-tering, without loss of accuracy and robustness of the system. In this methodology, called High Order Sliding Mode (HOSM) control, the n-th order system dynamics is reduced to a second or higher order dynamics, which is controlled by different control laws that do not cause chattering. This technique was proposed by Levant and Fridman (2002). The problem associated with the HOSM is that it requires the real-time estimation of the derivatives of the measured signal, what is corrupted with noise in real applications. So, robust differentiation techniques must also be applied, also derived by Levant (1998). The HOSM was applied to the DPS with promising results, either in numerical simulations (Tannuri and Agostinho, 2010) and small-scale experiments (Sousa Jr. and Tannuri, 2013).

4.1 Some illustrative results

The same experimental set-up presented in the Fig 12 and in the Fig 13 was used to verify the performance and robustness of the SM and HOSM controllers. Some illustrative results will be presented in this section, and a comprehensive description of the whole set of experiments are given in Tannuri et al. (2010) and Ferreira; Tannuri, (2013).

The robustness of the SM controller must be checked for variations in environmental conditions, as the mathematical model of the dynamics of the vessel is highly nonlinear. This aspect is experimentally verified by imposing different wind speeds during a heading maneuver (Fig 16). The tests were performed in both full and ballasted condition. A Pitot tube device measured the wind speeds and the values indicated are approximate. The results reveal that in ballasted condition, wind speeds larger than 2.5m/s caused saturation of the thrusters and position loss. The main performance parameters (overshoot, rise time) are shown in Table 5. Rise time is defined here as the time elapsed for a 15o rotation of the vessel (-180o to -165o). It can be seen that the parameters are quite similar for each loading condition, considering all wind speeds. This result is an evidence of the robustness of the controller to environmental action. It must be stressed that the same control parameters are used for both loading conditions.

The HOSM controller also demonstrated very good

performance and robustness properties, as indicated in Fig 17. Similar performance is obtained in the tests with and without environmental action. Besides the good behavior, both controllers (SM and HOSM) present an easy tuning procedure, and simple “rules of thumb” can be used.

Fig.16 SM controller - wind action - yaw maneuver: Full loaded condition (above); Ballasted condition (below).

Table 5 Overshoot and rise time - wind action.



Fig.17 HOSM controller - Ballasted vessel - Without wind (above); With wind (below).

5 Thrust allocation algorithm considering the thruster interference effects

The Thrust Allocation (TA) Algorithm should distribute the commanded force among the vessels thrusters. In order to guarantee the safety of the operation the vessels have more thrusters than the minimum required to generate the surge and sway forces and yaw moment. Therefore it is a redundant problem, which allows an infinite number of solutions. Given that the Thrust Allocation offers infinite solutions, it should be optimized in order to minimize the power consumed to generate the thrust (Jenssen, Realfsen 2006).

Since TA Algorithms are a mature subject, different methods have already been studied (Van Daalen et al. 2011, De Wit 2009, Sorensen 2009, Jenssen, Realfsen 2006, Sordalen 1997, Moberg, Hellstrom 1983), but none of them considered the interference effects, due to thrusters and thruster-hull interactions, which affects the net thrust generated by each actuator.

It has been noted that the interference effects on thrusters significantly affect the delivered thrust (Dang, Laheij 2004),

therefore they should be considered during DP operations. USP and Petrobras are participating on the TRUST JIP, a Joint Industry Project (more than 20 companies, including thruster manufacturers, vessel operators, ship-yards and engineering companies) aiming at improving the understanding of thruster-interaction effects during DP operations. One of the USP tasks in this project is to develop an allocation algorithm able to consider the interference effects.

The interference phenomena can be divided in two effects, the interaction between thrusters and hull, and the interaction among the thrusters (Ekstron, Brown 2002).

The interference between thrusters and hull depends on the shape of the hull and the location of the thruster. The main effect is caused by the drag of the thrusters’ jet stream along the hull of the vessel, decreasing the net thrust, as shown in Fig 18. The interference between thrusters happens when the same, usually azimuth thrusters, are close to each other. It is possible to observe the effects of drag and a decrease of efficiency, when one thruster works in the wake stream of another. Only the effects of physical proximity between thrusters are taken into account in this project.

Fig.18 Thruster and hull interference effect.

In order to represent quantitatively the interference effects, a polar efficiency function was suggested. Fig 19 represents the efficiency functions experimentally derived for the 6-azimuth thruster DP barge previously shown (Fig 10). The physical phenomena responsible for each efficiency reduction are also indicated. The experimental apparatus latter explained was used to obtain such efficiency functions.

5.1 The formulation of the thrust- allocation problem

The function that shall be minimized by the optimization algorithm is called Objective Function (Obj). This function is the sum of the power consumed by each thruster. Note that the consumption of power by a thruster is given by Power = l.T 2/3, where l is a constant value of the thruster and T is the developed thrust. Since all the thrusters are equal in the case study vessel (that will be presented in section 3), the Objective Function is:

(6)

In order to assure that the total forces commanded by the DP System (Fsurge, Fsway, Mway) are matched by the total forces generated by the set of actuators, a nonlinear constraint should be solved during the optimization process, given by:

(7)



This optimization problem is solved by a Trust Region SQP algorithm. A quadratic programming solver using Active Set Method (Nocedal and Wright 2006) is used as the basis for the Trust Region SQP. The processing time required for solving the optimization problem is about 0.2s in a conventional PC. Details about the numerical method can be found in Arditti and Tannuri (2012).

5.2 Experimental results

In order to test the new TA algorithm, an apparatus to measure the thrust developed by each thruster in different azimuth positions was used (Fig. 7). The equipment used to perform the test is composed by a load cell, a signal processing board, an AD converter, a computer, some test masses and a wireless transmitter and receiver to command the vessel from the computer.

A Forbidden Zone Algorithm was used for comparison purposes, since it is normally applied in DP Systems. It does not allow the thrusters’ water jet hit another thruster, defining an azimuth 20º forbidden zone for the thrusters #1 and #2, and for the thrusters #5 and #6. The Fig 21 shows the results for a commanded force of Fsurge = –7 N; Fsway = 7 N; Myaw = 0N.m. Other results are presented in Table 6. Note that the Commanded Force could be delivered by the Suggested Algorithm and the by Forbidden Zone Algorithm, with some small differences mainly related to the experimental accuracy.

Furthermore, the Proposed Algorithm saved 5% power (average) in relation to the Forbidden Zone Algorithm.

Fig.20 Experimental set-up.

Fig.19 Thruster efficiency curves for a DP barge.



Fig.21 Experimental results for Fsurge= –7 N; Fsway= 7N.

Table 6 Experimental Results (Forces in N, normalized Power).

Besides the reduced power consumption, the proposed TA algorithm has the advantage of being general, since it can deal with any source of interference problems, and also with propellers that are less efficient than others. However, it requires detailed information about the thrusters’ efficiency, obtained either by small scale experiments or CFD modeling.

6 Conclusions

A brief summary of researches related to DP Systems conducted at the USP in cooperation with Petrobras was presented in the paper.

Acknowledgement

The author thanks Petrobras, the Brazilian Innovation Agency (FINEP), the National Council for Scientific and Technological Development (CNPq) and São Paulo Research Foundation - FAPESP for the support to researches related to DP System.

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Abstract

The Design for Safety philosophy and the ensuing formalized methodology, Risk-Based Design, was introduced in the maritime industry in the mid-nineties as a design paradigm to help bestow safety as a design objective and a life-cycle imperative. This was meant to ensure that rendering safety a design driver, would incentivize the industry to seek for cost-effective safety solutions, in response to rising societal expectations for human life safety. It turned out that the removal of rules-imposed (largely-conservative) constraints and the adoption of a performance-based approach to address safety has had much more profound effects than originally anticipated, the full impact of which is yet to be delivered. This paper focuses on what constitutes the kernel of this design philosophy, namely the measurement and verification of safety itself with emphasis on passenger ships and the implications that this entails with regards to traditional approaches and the new safety system.

Keywords

Design for Safety; Risk-Based Design (RBD); Safety Measurement and Verification; Life-Cycle Risk Management

1 Introduction

Safety permeates all physical and temporal boundaries and as such it is the most influential factor in ship design and operation. Conversely, all human activity in a “risky” environment, such as the sea and in a fiercely competitive, tight-margins industry, such as the marine industry within a fast-changing, technology-intense world, is fraught with wide-ranging problems that tend to undermine safety. This calls for a “safety system” that is generic and flexible for ease of adaptation to change, holistic for ease of transcending complexity and sustainable for ease of gaining wider acceptance and support, thus providing a foundation for continuous improvement. Such requirements demonstrate the deficiencies of the current safety system (prescriptive) and the challenges that lie ahead. This is particularly true for knowledge-intensive and safety-critical ships, such as the giants of the cruise ship industry being built today, where the need for innovation creates unprecedented safety challenges that cannot be sustained by prescriptive-regulation-based safety. The reason for this is simple: traditional approaches to safety (rules-based) are experiential and with change happening faster than experience is gained, the “safety system” is unsustainable. This realization helps explain the need for changing the way safety is treated in the maritime sector.

The need to change the way safety is being dealt with is forcing the realization that the maritime industry is a “risk industry”, thus necessitating the adoption of risk-based approaches to maritime safety. This, in turn, is paving the way to drastic evolutionary changes in ship design and operation. Notable efforts to respond to these developments in the maritime industry led in 1997 to the

Maritime safety - to measure is to improve

Dracos VassalosThe Ship Safety Research Centre (SSRC), Dept. of Naval Architecture and Marine Engineering (NAME)University of Strathclyde, Glasgow, United KingdomE-mail: [email protected]



establishment of large scale (€150M) EU collaborative research to promote a new design philosophy under the theme “Design for Safety” with the view to integrating safety cost-effectively within the design process in a way that safety “drives” ship design and operation. This, in turn, led to the development and implementation of Risk-Based Design (RBD) in the maritime industry as the formal design methodology treating safety as a design objective rather than a constraint. The biggest impact has been at the International Maritime Organization (IMO) and by IMO: Safety Level, Alternative Design and Arrangements, Goal-Based Standards, to name but a few unprecedented new legislative instruments. The adoption of these, marks the beginning of contemporary safety, catalysing an impact, that is still being delivered.

Distilling understanding from such developments, certain truths emerge, which are becoming the guiding principles in incentivising and nurturing wider acceptance and ultimately industrialisation and exploitation of the concept. These include: • Risk-Based implies Performance-Based and this, in turn,

nurtures the use of scientific approaches and knowledge in all forms for safety performance evaluation in the ship design process;

• Ship operation is attracting focus as the arena for managing residual design risks and the conduit for monitoring safety and providing feedback to ensure that life-cycle changes are reflected in the way safety is managed, thus fuelling a system for continuous improvement;

• The dogma “to measure is to improve” is becoming the vehicle to address safety holistically and a life-cycle imperative.

It is this latter point that this paper focuses on as this constitutes the kernel of the “Design for Safety” philosophy, namely the measurement and verification of safety itself through the life-cycle of the vessel. Emphasis is placed on passenger ships and, in particular, damage stability, their “Achilles heel”.

2 Design for safety: risk-based design

By defining safety as the state of acceptable risk (Vassalos, 1999), the duality “safety and risk” becomes easier to apprehend and this facilitates understanding of all the ensuing concepts. In this respect, “Design for Safety” refers to a design paradigm introducing safety in design as another objective. This requires explicit consideration and quantification of safety, which is equivalent to evaluating risk during the design process; hence the term Risk-Based Design. Discussions at IMO over Goal-Based Standards have given rise to another term “Safety Level”, a wrong choice of terminology but it was meant to designate the through-life level of acceptable risk associated with a particular ship concept and, as such,

becoming the new guiding philosophy to attaining safety cost-effectively. What this entails, however, is no mean task; it is nothing less than being able to quantify the life-cycle risk of a vessel by considering all “passive” (design) and “active” (operational) safety measures and to do so during the concept design stage under extremely tight cost and time constraints. Application of RBD is biased towards design concepts with high levels of innovation. Hence the need to use knowledge in all its forms: best practice, engineering judgment, state-of-the-art tools and data, all part of Quantitative Risk Analysis (QRA).

The essential advance attributable to RBD is the holistic, explicit, rational and cost-effective treatment of safety. To achieve this, the following principles have been put forward (Vassalos, 2008):

1. A consistent measure of safety must be employed (risk) and a formalised procedure of its quantification adopted (risk analysis). For this to be workable, considering the complexity of what constitutes safety, a top-down approach is required with clear focus on major accident categories and Key Safety Performance Indicators (e.g., A-Index for damage stability and similar indices for fire, systems availability, evacuability, etc), all such performances captured with knowledge intensive models to enable fast and accurate safety performance evaluation and to facilitate optimisation studies.

2. Formal procedures for risk quantification, risk assessment and risk management, used in the marine industry include the Formal Safety Assessment (IMO FSA 2002) for generic risk assessment (at ship fleet level) and in support of the rule making process and the Safety Case of the Health and Safety Executive (HSE Safety Case 2005) for use in specific design/measures, among others. The right-hand-side of Figure 1 illustrates the elements of a typical “safety assessment process”.

3. Such procedure must be integrated in the design process to allow for trade-offs between safety and other design factors by utilising overlaps between performance, life-cycle cost considerations, functional requirements and safety. The interfaces between the ship design process and the safety assessment procedure are illustrated in Figure 1. Consequently, additional information on safety performance and risk will be available for design decision-making.

4. Considering the level of computations that might be necessary to address all pertinent safety concerns and the effect of safety-related design changes on the overall design performance, different handling of the design process is required. Namely, to allow for trade-offs between safety and other design objectives through overlaps at parameter level, the latter will also need to be addressed through the use of parametric models and access to fast, accurate and knowledge-intensive tools, access to databases (past designs, incident /accident data, etc.). Furthermore, the need for integration of all the tools and data under one umbrella (Integrated

Maritime safety - to measure is to improve Dracos Vassalos


Design Environment) to facilitate data and process management is paramount. Risk-based Design is by its very nature akin to holistic optimisation and use of formal optimisation and data analysis techniques essential to achieving optimum design solutions whilst ensuring cost-effective safety.

The aforementioned RBD principles are reflected in the following high-level definition: RBD is a formalized methodology that integrates systematically risk assessment in the design process with prevention/reduction of risk embedded as a design objective, alongside “conventional” design objectives. Put differently, safety rules give way to safety objectives, giving rise to additional functional requirements and design criteria and to the need for first-principles tools for verification of “safety performance”, in the absence of experiential knowledge. Key to understanding RBD is the integration of risk assessment in the design process and decision-making towards achieving the overall design goals but also as part of a parallel (concurrent) iteration within the safety assessment procedure to meet safety-related goals/objectives as depicted by the high-level framework of Figure 1. In relation to design decision-making, in the same way of using explicit ship performance evaluation criteria (design criteria) and economic “targets” (owner’s requirements), there is a need to define safety performance evaluation criteria and risk acceptance criteria. The latter could be related to safety performance criteria, so that safety performance could be used in the design iterations, alongside or even instead of explicit risk acceptance criteria. As a result, key design aspects of the initial baseline designs (watertight subdivision, structural design, internal layout, main vertical zones, bridge layout, materials, major ship systems, etc.) can be optimised from the point of view of ship performance, cost implications, potential earnings whilst ensuring that the safety level (as quantified) is appropriate and commensurate with acceptable risk levels (provided that such do exist).

Another key aspect to Risk-Based Design is that any ship design decision will be well-informed and will lead to design concepts that are technically sound (at least to a level commensurate with state-of-the-art), fit for purpose, and last but not least, with a known level of safety that is more likely (than by following rules) to meet modern safety expectations.

Fig. 1 A high level framework for risk-based design.

3 Life-cycle safety (risk) management (LCRM)

Safety and by extension Safety Management is a life-cycle process, starting at the concept design stage and continuing throughout the life of the vessel. In this process, safety must be continuously monitored and reviewed to ensure developments/changes in the design and its operation are reflected in the way safety is managed. The safety management process must be formal and transparent to allow the operator to nurture a safety culture and to manage safety cost-effectively. The formal process also facilitates measurement of safety performance, which contributes to the process of continuous improvement. This will fuel the requisite virtuous cycle shown in Figure 2. There are many elements that need to be addressed as indicated in this figure, including:

1. Safety Policy, describing the corporate approach to safety.

2. Safety Management Organizat ion, describing the management hierarchy relating to safety with responsibilities defined at each level.

3. Safety Management Strategy, outlining the high-level approach to safety management.

Fig. 2 A virtuous life-cycle safety management.

4. Safety Management Plan, describing the safety tasks to be targeted at each stage of the design.

5. Hazard Identification (HAZID), including details of when HAZID exercises should be completed and how these contribute to the safety case.

6. Risk Modelling, with details of the scope of the modelling and how it contributes to the safety assessment.

7. Risk Assessment, including quantitative and qualitative approaches, with guidelines on which is appropriate at each stage of the process.

8. Cost Benefit Analysis, including details of how to quantify the benefit of a risk reduction measure.



9. System of Continuous Improvement, ensuring that new hazards are identified, near miss incidents are considered and the SMS is kept up to date.

The first 4 steps point to the fact that safety management is an all-stakeholders affair. The next 4 steps relate to estimating the safety level at the design stage and the last step at addressing management of residual risk through safety performance monitoring and feedback. This brings to the fore the role of ship operation in life-cycle safety management, which deserves special attention.

This thinking is largely in line with the above-mentioned Safety Case and FSA approaches and more latterly the Guidelines on Alternative Design and Arrangements (MSC\Circ.1002, 1212) with the focus clearly on safety performance verification. The Safety Case approach to safety management is more ship-specific rather than ship type specific as in the case of the FSA. As such, it is treated as a “living instrument”, starting with the first concept of design and spanning the whole life cycle of the vessel. It starts with a suite of safety claims. As the design develops, the claims can be reinforced with arguments. When the design is finalized, the arguments can be verified with evidence. At the design stage, the evidence consists of results of relevant design safety verification activities (e.g., engineering analysis, model tests, etc.). These results are used to assess the risk level and verify that adequate measures are taken into account to ensure that residual risks (to be managed operationally) are acceptable. This is illustrated in Figure 3.

Fig. 3 Safety level estimation during concept design stage.

The focus on dealing with residual risks, naturally leads to the need for a SMS (Safety Management System), outlining the organization and procedures required to maintain an acceptable level of safety throughout the life of the vessel. This has to be aligned with the ISM (International Safety Management) Code implemented onboard. The formal process facilitates measurement of safety performance, which contributes to the process of continuous improvement. Pertinent activities include aspects of onboard and shore-based Safety Centres, monitoring systems and emergency decision-support for crisis management. Ultimately, all these feed into future newbuildings specification.

In line with the aforementioned principles and activities and in support of the Risk-Based Design paradigm, the overall goal is to develop a framework and the process to support life-cycle risk management. Key elements include:

• Integration of generic data and results (from FSA) into the concept design phase to establish baseline risk level

• Expedient evaluation of the ship safety level to facilitate integration of the safety assessment process into the ship design process

• Development and integration of a safety level monitoring system with the Ship Safety Management System and implementation of procedures effectively addressing and managing residual risk in normal ship operation and in emergencies.

• Continuous monitoring and improvement of all elements of the SMS. In practice, this will take the form of audits, safety case reviews and regular updates of the hazard log / risk register and risk model.

Elements of such a system already exist and others are being developed as part of newbuilding projects for leading cruise ship operators, as described in the next section. For this to become industry practice and standard will take time and effort.

4 Risk-based design implementation and LCRM

4.1 Design phase: safety level (total risk) estimation

A common way of presenting graphically the chance of a loss (risk) in terms of fatalities is by using the so-called F-N diagram, the plot of cumulative frequency of N or more fatalities, together with related criteria, Figure 4, (IMO MSC85 2009). In addition, some form of aggregate information is used, such as the expected number of fatalities E(N), often referred to as Potential Loss of Life, PLL. This is outlined next.

4.2 Risk model

(1)

Where, Nmax the maximum number of persons onboard and the FN curve is given as:

(2)

The frequency frN(N) of occurrence of exactly N fatalities per ship year is modelled as follows:

(3)



Fig. 4 FSA cruise ships – societal risk.

Where, nhz is the number of loss scenarios considered, and hzj represents a loss scenario, identifiable by any of the principal hazards. Furthermore, frhz(hzj) is the frequency of occurrence of scenario hzj per ship year, and prN(N|hzj) is the probability of occurrence of exactly N fatalities, given that loss scenario hzj has occurred. Table 1 shows estimates for the annual frequencies of occurrence for flooding- and fire-related hazards derived from statistics, (Jasionowski and Vassalos, 2006).

Table 1 Principal hazards.

Research effort is currently being expended to derive these from first principles. With passenger ships, flooding- and fire-related scenarios comprise over 90% of the risk (regarding loss of life) and almost 100% of all the events leading to decisions to abandon ship. Therefore, it would be possible to estimate the total risk (safety level) of a passenger vessel by addressing these two principal hazards alone in a consistent manner and framework, allowing for their contribution to risk to be formally combined as indicated in Figure 3 and in equation (3).

The specific design implementation highlighted here relates to the largest cruise ship ever built during the concept development phase, under the name Project Genesis, having the general particulars depicted in Figure 5 and Table 2 below.

Fig. 5 Project Genesis.

Table 2 Project Genesis Main particulars.

As this vessel represents a step change in the size of mega-ships, including some unique, innovative features, focusing on safety and adopting a risk-based design methodology came naturally; in fact the initiative was entirely that of the owner. The task in hand was no less than proving that Genesis is not only the largest ship ever built but also the safest and do so during the concept design stage commensurate with all other design goals and functional requirements. The procedure adopted to achieve this is briefly described in the following under four pertinent headings:

4.3 Flooding survivability analysis

For undertaking this analysis a complex geometric model was developed comprising 717 compartments and 1,160 openings, as depicted in Figure 6.

Fig. 6 Flooding analysis model for project Genesis.

Frequency Analysis ( frhz (hz1): Even though analysis targeted both collision and grounding related flooding, only collision is addressed here to allow comparisons between Project Genesis and the rest of the world cruise fleet. As records of 111 ship years of statistics, obtained from the owner, showed zero



occurrences of flooding incidents, the frequency of 1.48E-3 per ship year (1 event every 571 ship years), deriving from statistics of the existing cruise ships, Table 1, was used instead.

Consequence Analysis ( prN (N I hz1): The comprehensive risk model described in (Vassalos, 2008) requires two parameters to be estimated: the first is the time required for orderly evacuation of passengers and crew in any given event, derived from numerical simulations using advanced evacuation simulation software (Vassalos at al., 2003); the second is the time to capsize/sink, which is evaluated by sampling the random variables comprising loading conditions, sea states and damage characteristics (location, length, height, penetration according to the damage statistics adopted in the probabilistic rules) using Monte Carlo sampling and each damage scenario is simulated using explicit dynamic flooding simulation by PROTEUS3, (Jasionowski, 2005). The investigation involves a case by case explicit dynamic flooding simulation accounting for transient- cross- and progressive-flooding, impact of multi-free surfaces, watertight and semi-watertight doors. 342 collision scenarios were used resulting in an absolute sampling error for the cumulative probability of time to capsize of the order of 4%-5%. A typical set up of Monte Carlo simulations is shown in Figure 7 (generic) and Figure 8 for Project Genesis collision studies. A comprehensive experimental programme was also set up to verify the numerical simulations, offering corroborative evidence and hence confidence in the derived results, which are presented in Figure 9 as an F-N curve together with results from the FSA on cruise ships (IMO MSC 85, 2009).

The results clearly demonstrate the superior flooding survivability characteristics of Project Genesis.

Fig. 7 Monte Carlo simulation – collision.

Fig. 8 Monte Carlo simulation set up – collision.

Fig. 9 Societal risk – collision accidents.

4.4 Fire safety analysis

A full description of the risk model developed for fire safety analysis can be found in (Vassalos, 2008). The general set up is illustrated in Figure 10 next. The ship has 144 fire zones, 80 in excess of SOLAS.

Fig. 10 Fire risk model illustration.

Frequency Analysis ( frhz (hz2): A fire incidents database was provided by the owner containing 577 fire incidents (including near-misses) in 111 ship years of records. This was used to derive a simple numerical model for fire occurrence in any given space onboard the ship based on frequency per unit area for each type of space.

Consequence Analysis ( prN (N I hz2): Empirical data was used to develop design fires for each type of space onboard and fire dynamics calculations to estimate the time evolution of the fire in both enclosed and external spaces. Similar to flooding cases, escape time simulations were also undertaken to estimate impact on occupants. A total of 8,326 fire scenarios were evaluated in 144 fire zones (8 main vertical zones and 18 decks) for night and day occupancy cases. The results are presented in Figure 11 as societal risk, together again with results from the FSA on cruise ships. The superior fire safety characteristics of project Genesis are clear to see.

With flooding and fire modelled consistently using the same framework, the risk contributions from each hazard can be combined, thus giving what constitutes (almost) the total risk for Project Genesis, as shown in Figure 12 together with the corresponding result from the IMO cruise ship FSA.



Fig. 11 Societal risk - fire and explosion accidents.

In addition to the foregoing considerations, a number of specific regulatory and other safety issues were considered as outlined briefly in the following.

Fig. 12 Societal risk – project genesis vs existing fleet.

4.5 Alternative designs (equivalent safety)

• Large fire zones, average 1,950 m2 designed to SOLAS Ch. II-2 Reg. 17 and Guideline MSC/Circ. 1002

• Openings in main fire bulkheads with A-60 roller shutters (Royal Promenade)

• Fire breaks on open areas between split superstructure

• LSA: Enhanced functionality large lifeboats – Rescue Vessels (18 life boats for 370 persons each); 4 MES Stations for 450 persons each.

4.6 Dynamic behaviour at sea

• Extensive model tests with full-scale verification, including: life boat tests; weather criteria tests; wave excitation measurements on rigid and segmented models; parametric rolling; behaviour in F/Q seas; manoeuvring calculations / simulations and model tests.

4.7 Safe return to port

• Systems related to propulsion, covering also steering and

manoeuvring capability ( + fire, flooding, navigation)

• Systems related to comfort

4.8 Additional safety and security features

• Dedicated Safety Centre within bridge

• Improved focus on navigation

• Improved ability to manage safety and security incidents

• Dynamic Positioning

• Improved systems for emergency mustering

• Comprehensive digital CCTV system

4.9 Operational Phase: Management of Residual Risk

Having achieved the goal of designing a safe ship cost-effectively and to go beyond all new and emerging safety requirements by utilizing all available knowledge and technology, the question that came naturally to the fore is whether this extensive knowledge acquired during the design phase could be used to manage operational / accidental risk over the life-cycle of the vessel. More importantly, the goal post could be set even higher, namely to target optimum balance between safety and operational efficiency. Tackling such questions and concerns as watertight doors, ballasting/de-ballasting, damage control and so on led to the development of iStand (illustrated in Figure 13), a Decision Support System (DSS) installed onboard the first ship of the Genesis series with the following general features – in addition to being a standard onboard loading computer:

1. Real time sensors and hardware integration (link to ship’s SMS): tank levels, draughts, door states, water ingress alarms, wind and waves. Any change in ship loading or internal architecture is being continuously monitored.

2. Vulnerability log: Global and local ship vulnerability to flooding - monitoring the flooding-related risk onboard to any changes in related ship or environmental parameters. Vulnerability to fire is undergoing development.

3. Criticality assessment: survival time, escape and evacuation time (crisis management)

4. Corrective action search: evaluation of the impact of corrective actions. Ballast system availability.

5. Essential systems availability post-flooding: verification of compliance with Safe Return to Port requirements.



Fig. 13 Screenshot of iStand (onboard decision support system).

The DSS developed comprises a very powerful computer with a massive database encapsulating all the features of Safe Return to Port Requirements and linked to sensors capable of monitoring all the elements that could affect ship vulnerability.

4.10 Emergency response: preparedness / crisis management

In support of a life-cycle risk management thrust, the first two elements of the DSS provide for monitoring of ship operation and feedback functions whilst 3 to 5 provide internal capability for handling emergencies. Moreover, the on-board experience gained to date provides invaluable information to guide improvements in the design for the next generation of cruise ships. Emergency response is the last line of defense in life-cycle risk management and given the potential time constraints in an emergency, emphasis in developing and familiarizing crew with emergency response procedures is paramount. This brings to the fore the need for continuous monitoring, a key element to preparedness. Equally as important is the ability to provide the master with clear cut advisory related to managing a crisis. All these are elements currently under development by leading cruise ship operators.

Fig. 14 Screenshot of iStand (emergency response - crisis management).

5 Concluding remarks

Based on the review of development and implementation of RBD, the following concluding remarks can be drawn:

• Life-cycle Risk Management is a formal process providing a holistic framework, to embrace all phases of the life-cycle of the vessel from design (risk reduction/mitigation) to operation (management of residual risk) and emergency response (preparedness/crisis management), leading to safety assurance in the most cost-effective way possible.

• Such a formal process facilitates measurement of safety

performance, which constitutes the kernel for continuous safety improvement and the foundation for instigating and sustaining a safety culture in the maritime industry.

Acknowledgements

Most of the work presented here represents shared aspirations and developments with a number of colleagues from Safety at Sea Ltd, a consulting company in Glasgow, part of the Brookes Bell Group. The support received over the years by the European Commission in undertaking part of the research work presented here is gratefully acknowledged. The author would also like to express his appreciation and sincere thanks to the maritime industry and, in particular, to RCCL for offering him the unique opportunity of being part of the design team in a number of ground-breaking projects and for using the material presented in this paper. The continuing support of researchers and staff at SSRC and NAME is gratefully acknowledged.

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IMO MSC 85 (2009), “FSA Cruise Ships”, submitted by Denmark.

JAsionowski, A., Vassalos, D. (2006), “Conceptualising Risk”, 9th International Conference on Stability of Ships and Ocean Vehicles, Rio de Janeiro.

vAssAlos, D., Guarin, L., Vassalos, G., Bole, M., Kim, H.S., Majumder, L. (2003), “Advanced Evacuation Analysis – Testing the Ground on Ships”, 2nd International Conference on Pedestrian and Evacuation Dynamics, PED 2003, Greenwich, London.

JAsionowski, A. (2005), “An integrated approach to damage ship survivability assessment”, PhD, University of Strathclyde.

IMO (2003), MSC77/INF.12 - SAFEDOR . Risk-Based Design, Operation and Regulation of Ships.



MS&OT – Guidelines for Authors

Title of paperFirst Name Surname,Organisation,Addressofcorrespondingauthor(includinge-mail)

AbstractTheabstractshouldbeabriefdescriptionofthescopeofthepaper,notexceeding100wordsinlength

Keywords:atleast3suitablewordsforindexingpurposes

NomenclatureAnomenclatureisrequiredforpapersusingalargenumberofsymbols,abbreviationsandacronyms.Wherepossible,theseshouldbeorderedalphabetically.

Symbol1 DefinitionSymbol2 Definitionetc.

E.g.:α Angleofattackr Densityofwaterl Wavelength

1. IntroductionThisisnormallythefirstsectioninthemainbodyofthetext.Pleasenotethatthissectionandallsubsequentsectionsandsubsectionsarenumbered.Allmainheadingsshouldbetypedinboldasshownbelow.

2. Heading

2.1 Sub-headingEachSectionmayhavesub-headings.Sub-headingsshouldbenumberedandtypedusinglowercaseasabove.

2.2 Sub-heading

2.2 (a) Further subsidiary heading Thesub-sectionscanbefurtherdividedupasabove.Furthersubsidiaryheadingsnotinboldinlowercase.

3. Manuscript format conventions

3.1 FontThefontstobeusedarethesamethathavebeenusedforthispage,TimesNewRomanandArial.Thetitleofthepapershouldbein12pointboldcapitals.Authorsnamesshouldbein10pointbold,withaffiliationin10pointregular.Therestofthepapershouldbein10pointusingthefontstyleindicatedinthistemplate.

3.2 Page setupThefinalmanuscriptshouldusethestyleusedinthistemplate.ThemarginsareasfollowsforbothA4andUSletterstyleinorderthatAcrobatversionsofthemanuscriptcanbeprintedoneitherA4or8.5x11inchpaper:

A4 8.5x11 in.

Top 2.5cm 1.0in

Bottom 3.5cm 0.7in

Left 1.7cm 0.8in

Right 3.5cm 0.7in

70 Marine Systems & Ocean Technology

3.3 Page numbersPleaseputpagenumbersonmanuscriptatbottomcenter.Thiswillberedonebytheeditorsinthefinalprintedversion.Totalheightofprintedmaterialsincludingpagenumbersequals23.7cmor9.3inches

3.4 Figures

3.4 (a) General guidelinesAllillustrationsshouldbeclearlyreferencedinthetext

Figuresshouldbeplacedinthemainbodyofthetext.

Textwithinfiguresshouldbeofasizetoallowlegibilityevenifreduced.

Figuresmaybeincolororinblackandwhite.Ifyouusecolorgraphicspleasecheckthegraphicinblackandwhitetosee ifshadingorhatchingisneeded.Whereverpossible,figureswillbeinblackandwhite.

Captionsforillustrationsshouldbetypedunderneatheachfigure.

3.4 (b) Figure formatFiguresshouldbeproducedelectronicallywherepossible,in.wmf,.eps,.jpg,.cdr,.gif,or.tifformats.ExcelchartsshouldbecopiedandpastedtoMicrosoftWord.Saveanothercopyofeachindividualgraphicinseparatefile(Fig1,Fig2,etc.)inadditiontothecom-pletemanuscriptfile.Theresolutionshouldbeatleast300dpi,andpreferablyabove500dpi.

Pleaseensurethattheletteringusedintheartwork/illustrationsdoesnotvarytoomuchinsize.Thefinalfontsizeshouldbeabout6-8point.MakesurethatthephysicaldimensionsofyourartworkmatchthedimensionofA4paper.

4. Submission requirementsAuthorsmustsubmittheirpaperINELECTRONICFORMATinwordprocessororAcrobatformat.TheymustbesenttooneoftheEditors.

Papersshouldbesentase-mailattachmentsifeachfileisnolargerthan3MB.

Iflargerthan3MB,aCDshouldbesenttotheEditors.

Maximumlengthofpaper20pages(above20,witheditorsapproval).

IfthereisanypossibilitythatcertainsymbolsmaynottranslatetoanEnglishversionofMSWordortheAcrobatversionmay havemissingimbeddedfonts,2hardcopiesoftheirprintedmanuscriptshouldbesenttotheEditorssothatpropereditingto Englishsymbolscanbedone.

5. Additional information for authors

5.1 LiabilityAuthorsareresponsibleforobtainingsecurityapprovalforpublicationfromemployersorauthoritieswherenecessary.Iftheysowish,authorsshouldincludeadisclaimerattheendofthepaperstatingthattheopinionsexpressedarethoseoftheauthorandnotthoseofthecompanyororganisationthattheyarerepresenting.

6. ConclusionsThemainbodyofthetextshouldendwiththeconclusionsofthepaper.

AcknowledgementsBriefacknowledgementsmaybeadded.

ReferencesReferencesshouldbelistedalphabeticallywiththeyearofpublicationjustaftertheauthor’slastnameaandreferredtointhetextasFirth(1989):

Firth,S.(1989)-“InvestigationintothePhysicsofFree-RunningModelTests”.SNAMETransactions,pp.169-212.

Marine Systems & Ocean Technology 71

72 Marine Systems & Ocean Technology

Calendar of Events

IDS 2013First International Conference IDS2013 - AmazoniaIquitos, Peru, 17-19 July 2013 www.ids2013.pe

ISSW 201313rd International Ship Stability WorkshopBrest, Franc, 23-26 September 2013http://issw13.sciencesconf.org/

COPINAVAL 2013XXIII Pan-American Conference on Naval Engineering, Maritime Transports and Port EngineeringMargarita, Venezuela, 30 September-04 Octoberwww.ipen.org.br

IMAM 201315th International Congress of the International Maritime Association of the MediterraneanLa Coruña, Spain, 14-17 October 2013www.imamhomepage.org/imam2013/

PRADS 201312th International Symposium on Practical Design of Ships and Other Floating Structures, CECO, Changwon City, Gyeongnam, Korea, 20-25 October 2013www.prads2013.org

SNAME 2013 Annual MeetingHyatt Regency, Bellevue, WA, 6-8 November 2013www.sname.org

The Sociedade Brasileira de Engenharia Naval (SOBENA) is the Brazilian forum for exchange of theoretical and practical knowledge amongst naval architects and marine engineers. It was founded in the beginning of the modern phase of Brazilian naval construction, in 1962, with the aim of bringing together engineers, technicians and other professionals involved in activities as: shipbuilding and ship repair, design and other engineering services, maritime transportation, waterways, ports, specialized cargo terminals, ocean and river transportation economics, marine environmental protection, offshore support bases, offshore logistics, naval aspects of offshore exploration and production, construction and conversion of platforms and other offshore vessels.

SOBENA is a non-profit civil society, declared a federal public utility by Decree No. 97589/89, which since its foundation is aimed at promoting technological development in the above activities through courses, conferences, seminars, lectures and debates. SOBENA is a source of reference called upon to provide its opinion on matters of public interest and has also been politically active, expressing its views concerning topics of national relevance related to its areas of activity.

Following the evolution of the industry in the past years, SOBENA has started to include activities related to offshore oil exploration and production, holding events for professionals of those areas. As a member of the Mobilizing Committee of the National Petroleum Industry Organization (ONIP), SOBENA has been taking part in various subcommittees which are seeking to create conditions to promote the development of the Brazilian naval and offshore construction industry.

SOBENA has signed affiliation agreements with the Institute of Marine Engineers (IMarEST), with headquarters in London, England and cooperative agreement with The Society of Naval Architects and Marine Engineers (SNAME), from the United States of America.

CEENOCentro de Excelência em Engenharia Naval e Oceânica

The Centre of Excellence in Naval Architecture and Ocean Engineering (CEENO) was created in 1999 as a result of a joint initiative of four Brazilian institutions (COPPE, IPT, PETROBRAS and USP), traditionally involved in scientific and technological development applied to marine activities.

As a Centre of Excellence, CEENO aims to integrate facilities and human resources, developing theoretical and experimental methods, giving strong support for consolidation, expansion and improvement of the maritime activities in Brazil and worldwide.

CEENO has been involved in relevant projects on Offshore Engineering and Ship Design & Construction.

SOBENA Sociedade Brasileira de Engenharia Naval

President Floriano Carlos Martins Pires Jr.

Vice-President Luis de Mattos

Regional Director - São Paulo

Hélio Mitio Morishita

Administrative Director

João Carlos dos Santos Pacheco

Financial Director

Luiz Carlos de A. Barradas Filho

Technical Director

Murilo Augusto Vaz

Regional Director - São Paulo

Hélio Mitio Morishita

Associated Directors

André de Souza Manhães

Thiago M. C. Lembruger Porto

Luiz Felipe Pimentel M. de Araújo

Address:Av. Presidente Vargas, 542 - Gr. 713

Centro - CEP 20071-000

Rio de Janeiro - RJ - Brasil

Telephone: [+55](21) 2283-2482

E-mail: [email protected]

Site: www.sobena.org.br

list of editors - sobena · list of editors celso pupo pesce universidade de são paulo ... the aim...

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