Verification of damage ship survivability with …...Proceedings of the 17th International Ship Stability Workshop, 10-12 June 2019, Helsinki, Finland Verification of damage ship survivability

Proceedings of the 17th International Ship Stability Workshop, 10-12 June 2019, Helsinki, Finland

Verification of damage ship survivability with computationalfluid dynamics

Athanasios Niotis, MSRC, NAOME, Glasgow, [email protected] Vassalos, MSRC, NAOME, Glasgow, [email protected]

Evangelos Boulougouris, MSRC, NAOME, Glasgow, [email protected] Cichowicz, MSRC, NAOME, Glasgow, [email protected]

Georgios Atzampos, MSRC, NAOME, Glasgow, [email protected] Paterson, MSRC, NAOME, Glasgow, [email protected]

ABSTRACT

In the new era of direct stability assessment (DSA) for ship survivability in intact and damagedconditions, direct and accurate evaluation of the safety level achieved by the design plays a vital role. Two arethe most popular methods for DSA namely, time domain numerical simulation (TDNS) and ComputationalFluid Dynamics (CFD). Both can be used for the evaluation of the safety level of a ship post casualties,following collision or a grounding incidents. It is common practice for the TDNS methods to have as a core ahydraulic model for capturing the propagation of the floodwater and its dynamics in order to reduce thecomputational cost. However, more recently, CFD methods have matured enough to provide a crediblealternative, particularly concerning the investigation of complex fluid dynamics problems. The catch, however,is higher computation costs and this is where ingenuity helps. This paper proposes and demonstrates thefeasibility of using high fidelity computational fluid dynamics tools for direct damage stability assessment ofships.Keywords: damaged ship, numerical tank, survivability verification, CFD, OpenFOAM.

1. INTRODUCTIONThe survivability of a ship after damage has been

in the forefront of interest of the maritimecommunity for almost six decades. Accidents of thepast with devastating consequences in terms ofhuman loses, environmental damage and financialcost have raised the alarm in the area of maritimesafety. Engineers and scientist have been trying toinvestigate this complex hydrodynamic challengeusing as main tools model experiments andnumerical simulations.

Until the 1980s, the primary way to investigatethe behaviour of a ship after damage was by modeltesting. However, limitations such as facilityavailability, cost, time, and physical constraints(e.g., scale effects and dynamic similarity)encouraged the development of mathematicalmodels and numerical tools, which capture thephysics accurately and to study allow to study theproblem by means of numerical simulations.

Time domain simulation of flooding afterdamage is a very intriguing theoretical and

engineering challenge, which started beinginvestigating numerically since the 1980s at theUniversity of Strathclyde in Glasgow. The maindifficulty in this inquiry stems from the coupled non-linear dynamics between ship and floodwater, withcomplex interactions between ship, floodwater andenvironmental conditions.

The first time-domain simulation model wasintroduced by Spouge, 1985, for the investigation ofthe European Getaway accident. The ship motionwas calculated by a quasi-static approach and thefloodwater ingress with a hydraulic model.Vredeveldt & Journee in 1991 used hydraulic flowassumption coupled with one degree of freedom(DoF) dynamic roll motion model, which laterexpanded to a non-linear six DoF model (Journee,Vermee, & Vredeveldt, 1997). In their workVassalos & Turan, 1994, developed a 3DoF dynamicmodel for the simulation of the behaviour of roropassenger vessels in irregular waves. One year later,the first 6 DoF model for the dynamics of a ship afterflooding was introduced by the work of Letizia &Vassalos, 1995 & Vassalos D. , 2000. Papanikolaou

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http://cbs.wondershare.com/go.php?pid=2990&m=db


and Spanos introduced a lumped-mass model for thesimulation of the floodwater dynamics inside thedamaged compartment (Zaraphonitis, Papanikolaou,& Spanos, 1997; Spanos & Papanikolaou, 2001;Papanikolaou & Spanos, 2002). Santos & Soares, in2006 used shallow water equations for the modellingof the floodwater behaviour. Ruponen, in 2007,developed a pressure correction technique based onthe hydraulic model assumptions for the floodwaterpropagation in the internal spaces of the ship, whichis represented as a hydraulic network.

The majority of the methods, which have beenproposed are based on coupling hydraulic models forthe floodwater propagation with quasi-static ordynamic models. Furthermore, the equations of shipmotions are often linearized and based on theimpulse response technique for transforming theresults of the potential flow frequency domain to thetime domain (Cummins, 1962). The fundamentalassumptions of these models and the complexity ofthe phenomenon in question still leave someuncertainties regarding the capturing of its crucialcharacteristics, especially in the transient phase offlooding, which can profoundly influence thesurvivability of ships after damage (Vassalos, et al,2003).

On the other hand, the astonishing theoreticaland technological advancements in the field of CFDallowed researchers to use grid based RANS solversor mesh free CFD techniques for the simulation offlooding of a ship after damage (van't Veer & de Kat,2000; Strasser, Jasinowski, & Vassalos, 2009;Sadat-Hosseini, et al., 2012; Gao, Vassalos, & Gao,2010; Shen & Vassalos, 2011; Skaar & Vassalos,2006). However, their complexity andcomputational cost rendered the systematic use in amore systematic manner infeasible.

This work attempts to demonstrate the utilisationof CFD techniques for direct damage stabilityassessment and the survivability of ships afterdamage. Furthermore, it discusses challenges,limitations and opportunities in the directcomparison between high fidelity numerical fluiddynamic algorithms and time-domain simulationtools in the problem at hand.

2. TIME-DOMAIN SIMULATIONThe time-domain simulation software, which has

been used in this work is PROTEUS3 (Jasionowski,2001).

The three main elements in the time-domainsimulation of the motion of a ship after damage arethe mathematical description of ship motion, thefloodwater ingress and dynamics, and theenvironmental conditions, which influence thebehaviour of both ship and floodwater.

Ship DynamicsThe mathematical description of ship motions is

based on six degree of freedom rigid body motionequations, which derive from the conservation oflinear and angular momentum.

Figure 1: The coordinate systems used in the analysis.

The modelling of rigid body dynamics, involvesthree coordinate systems. An earth-fixed inertialframe of reference is assumed in point E withaxes . The second, inertial reference systemhas its origin at point (usually placed at theintersection of the midship section, with the centreline plane and the waterline plane of the intact vesselat calm sea), local axis and it moves with theaverage velocity of the hull.

The equations of motion of the ship are solvedbased on a third reference system attachedto the centre of gravity of the intact vessel.

The motions of the ship are described by twovector equations, derived from the conservation oflinear and angular momentum respectively(Jasionowski, 2001).

= (1)

= (2)

Where, and are the external forces andmoments acting on the body in respect to the Oxyzframe of reference. The linear momentum of thetranslating body and the angular momentumrelative to the same coordinate system are

= ∙ (3)

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= × ∙ (4)

Where is the finite mass of the rigid body, itsvelocity and its position vector with respect to the

.The total mass of the vessel in each time instant

is the sum of the intact ship mass and the totalfloodwater mass , which is equal with theaddition of the floodwater mass in each individualcompartment , ∑ .

= + = + (5)

Assuming that the floodwater mass in eachcompartment is concentrated to its centre of gravitythe equations (3) and (4) are equal with

= ∙ + ∙ (6)

= × ∙ + × ∙ (7)

where, , the position and velocity vectors ofthe centre of gravity of the intact ship mass withrespect to the coordinate system, and ,the position and velocity vectors of the centre ofgravity of each floodwater mass in respect to thesame coordinate system.

The final equations of linear and angularmomentum equations as derived form the (6) , (7)after the trnasformation of the frame of referenceform the to the are (Jasionowski,2001),

∙ + 2 ∙ ×

+ ∙ × +

× ( × )

+ ∙ ( + × ) (8)

+( + ) ∙ + ∙ +

× ( + ) ∙ =

( + ) ∙ + ∙ ×

+ ∙ [( × ) × ]+ ∙

+ ∙ × + × ( + ) (9)

+ ∙ [ × ( + )]

+ × ( + ) ∙ =

In the equations (8) and (6) the force and themomentum and are calculated in the body fixedreference system .

The external forces and moments are determinedbased on the supposition of the following hydrostaticand hydrodynamic entities: Froude-Krylov forcescalculated with body exact formulation; radiationand diffraction forces calculated in the frequencydomain using linear potential theory and thentransferred to time domain with the incorporation ofconvolution and spectral techniques (Vassalos D. ,2014). These forces pre – calculated for a range ofloading conditions, speed and headings; and thevalues are stored in a hydrodynamic database.During the time-domain simulations theinstantaneous values interpolated from the database.

Floodwater ingressThe floodwater ingress and propagation use

hydraulic models. The volumetric flow rate iscalculated, based on the Bernoulli equations as afunction of the difference of the hydrostatic heads ℎbetween sea and damaged compartment (Vassalos,Turan, & Pawlowski, 1997).

= ∙ ∙ 2 ∙ ∙ ℎ ∙ (10)

Where, is a pressure loss coefficient, theeffective area of the opening and the accellerationof gravity.

3. CFD FOR FLOODING SIMULATIONA step change in the investigation of

survivability of a ship after damage comes from theapplication of CFD techniques for the analysis ofthis problem. However, despite impressivedevelopments in the field of numerical fluidmechanics, the computational cost remainssignificant. For this reason, high fidelity CFDalgorithms are used selectively, for the treatment of

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specific issues that simplified time-domainsimulation models cannot capture.

The flooding process after collision or groundingcan be divided into three stages: transient,progressive flooding, and stationary-state (Vassalos,Jasionowski, & Guarin, 2006; Jasionowski,Vassalos, & Guarian, 2004). The peculiarity of thisproblem is that each stage requires a different levelof detail in its physical modelling.

Figure 2: Flooding stages of a ship after damage.

CFD for transient floodingWhen a ship or floating structure suffers from a

breach on her hull, the very first moment of theincident is characterised by the complexhydrodynamics equilibrium. The pressure gradientin the vicinity of the damage opening prompts thegeneration of a high momentum fluid jet. Theaccurate capturing of the impact of the jet is vital forthe assessment of the survivability of the vessel intransient response. The momentum of the jet isinfluenced by the hydrodynamic pressure at theopening, the geometry of the damage and the internalarrangement that receives the impacting jet. Highfidelity CFD tools can provide critical insight intothe complex hydrodynamics of this stage thatsimplified hydraulic models cannot capture.

CFD for progressive floodingThe next stage of the flooding process is the

propagation of the floodwater in the vicinity of thedamaged compartments through internal openings.The course of this stage is highly influenced by thewatertight and non-watertight subdivision of thevessel as well as the sea condition. The problem canbe closer to a hydraulic network routing in case ofships with a complex arrangement such as cruiseships or a hydrodynamic nature in the case of shipswith large undivided spaces, such as the car deck ofRoPax vessels. A key element for the accurate

prediction of the survivability of the ship, during thisstage, is her response to waves. In the final stages ofthe progressive flooding and before the stationarystate condition the fast, simplified models have anadvantage as the nature of the problem is drivenlargely by hydraulic energy rather than thehydrodynamic momentum. Still, CFD models cangive a better insight into the impact of various designdetails, which influence the outcome of the incident.Examples include the collapse of watertight doors,the influence of the arrangement of the openings, anda better prediction of the motions of the vessel undervarious environmental conditions.

4. LIFE-CYCLE FLOODING RISKASSESSMENT FRAMEWORKThe Life-Cycle Flooding Risk Assessment

Framework introduces a coherent decision-makingrationale for the evaluation of the safety level of aship against flooding. This approach entails thesurvivability assessment of the ship after floodingduring the design phase, the operational phase andthe emergency response phase, each of them havingdeferent safety objectives and employs differenttools (Vassalos, et al., 2018).

A primary characteristic of this approach is thatit evolves as the design and the operation of thevessel unfolds. The initial stage of the design startswith static vulnerability assessment and as the designprocess unfolds and becomes more detailed theassessment changes in nature and becomes dynamicwith the use of time-domain simulation tools. Theassessment finally is verified with the incorporationof CFD tools, which are used for vulnerabilityassessment and verification in critical scenarios.

Static Vulnerability Screening (SVS)The static vulnerability screening stage includes

the probabilistic damage calculations based on thecurrent SOLAS accident statistics. The output fromthis stage is the most critical scenarios which pass tothe next stage of the dynamic vulnerabilityscreening. The demarcation of the critical cases isbased on the hydrostatic properties at the equilibriumposition as it judged by the SOLAS regulations.

Dynamic Vulnerability Screening (DVS)After the identification of critical scenarios, the

time domain simulation tool Proteus3 is employedfor the dynamic survivability assessment of the shipin waves. The investigation will be performed for

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various operating and environmental conditions. Theidentified vulnerabilities can be either limited bydesign solutions or watertight door management anddamage control options.

Verification & Approval (V&A)This stage incorporates the use of a numerical

wave tank based on high fidelity CFD tools for theverification of the survivability of the ship in criticaldamage scenarios. The process includes:1) Identification of critical cases from DVS2) Numerical wave tank set up3) Execution of simulations4) Uncertainty analysis of the results5) Submission to the authorities for approval.

5. VERIFICATION OF TIME-DOMAINSIMULATION WITH CFD

Governing equationsFor the development of a numerical tank for the

verification of survivability of ships after damagewith high fidelity CFD tools the OpenFOAM, anopen source CFD toolbox, is used.

The governing equations for unsteady,incompressible, isothermal, viscus two-phase floware given by the Navier – Stokes equation (Ferziger& Peric, 2002; Moukalled, Mangani, & Darwish,2016).

∇ ∙ = 0 (11)∂( )

+ ∇ ∙ ( )

= −∇ + ∇ ∙ ++

(12)

Where, is the density of the fluid, thevelocity vector, the pressure, the stress tensor,

the gravitational acceleration, and the force dueto surface tension which in the specific engineeringproblem can be assumed negligible. As the flow isassumed incompressible, the density is constant sothe momentum equation is transformed into:

∂+ ∇ ∙ ( ) = −

∇

+∇ ∙ (∇ + (∇ ) )(13)

Where, = + ℎ the total pressure and= + the effective viscosity which

takes into account the turbulence model. For moredetails please see references (Damian; Foundation,2014) and the source code.

For the determination of the interface betweenwater and air, the volume of fluid model (VoF) isimplemented (Jasak H. , 2017). With the assumptionof one continuum medium in the problem domainthe VoF includes one more unknown scalar whichis defined as the volume of fraction between the airand the water. Assuming that the volume of fractiondefined as

0 ≤ ≤ 1 (14)Where, = 0 refers to the air, = 1 refers to

water and 0 < < 1 refers to the transitional regionbetween the two fluids. The volume of fluid methodintroduces one more governing equation which is thescalar transport equation of the volume fraction ,defined as,

∂+ ∇ ∙ ( ) + ∇ ∙ (1− ) = 0 (15)

Where, ∇ ∙ (1− ) is an anti – diffusionterm used to sharpen the interface in the parts of thedomain where there is a transition between the twophases (So, Hu, & Adams, 2009). The velocity isdifined as the relative velocity between water andair.

Figure 3: Survivability assessments of a ship after floodingduring the design phase (Vassalos, et al., 2018).

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The VoF model introduces the assumption ofone medium in the field with density and viscosityequal with,

= + (1− ) (16)

= + (1− ) (17)

where, and the value of the density andviscosity of the fluid .

Figure 4: Volume of fluid interface capturing method(Davidson, Cathelain, Guillemet, Huec, & Ringwood, 2015)

Finite Volume MethodThe governing equations of the motion of fluid

should be discretized in time and space for thenumerical solution of the flow variables. FiniteVolume Method (FVM) is the preferablediscretisation technique as it is a well-establishedmethod in the field of computational fluid dynamics(Moukalled, Mangani, & Darwish, 2016).

The significant advantage of the FVM is the useof integral representation of the governing equationswhich fulfil easier the conservation laws offundamental physics (Moukalled, Mangani, &Darwish, 2016). For this reason, this discretisationtechnique is popular for engineering applicationwhich encompasses complex geometries andcomplex fluid dynamics. After the discretisation ofthe problem domain in a computational grid of finitevolumes, the method uses the Gauss Theorem totransform the volume integral into surface integrals.Introducing a new scalar variable as thevolumetric flux through the surface of the cells theflow is described for the following equation

∂( )+ ∇ ∙ ( ) = ∇ ∙ ( ∇ ) + (18)

Which, are solved numerically with theincorporation of techniques which will be presentedin the next section.

Discretisation for Flooding SimulationOne of the biggest challenges in the grid-based

computational fluid dynamic techniques is thegeneration a proper gird representation of thedomain under investigation (Jasak H. , 1996). Thespace discretisation approach is a vital pre-processing step, as the mesh should have theappropriate level of detail to capture the geometry ofthe domain and, the underlying physical phenomena.Generally there is not rule of thumb, and theinvestigators should choose a discretizationtechnique based on the balance betweencomputational cost and desired accuracy(Foundation, 2014).

In the problem of flooding of a ship after damagethe following parts of the domain need specificattention:

Region of Damage and Internal OpeningsThe damage openings and the compartment

openings in the case of ship flooding simulationintroduce a geometrical constraint in the meshingprocess. The cell size should be small enough inorder to capture the geometrical details reassuringthe accurate representation of the engineeringproblem.

In addition to geometry definition thediscretisation in the vicinity of the openings shouldhave adequate volumetric extent, as in this area highvelocity and pressure gradients especially in thetransient and the progressive flooding stage of thesimulation are expected. The level of refinement inthese areas influences the total number of meshelements, the computational time and the accuracyof the solution.

Hull RegionIn case of the simulation of the motion of a ship

in intact or damage condition, the currentgeometrical representation of the hull underinvestigation has crucial importance for the fidelityof the numerical solution. The mesh element size onthe surface of the hull is influenced geometricallyfrom the curvature and the complexity of the surface.Form the physics point of view the element sizeshould be chosen based on + value as it is definedby the law of the wall for turbulent flow (Moukalled,Mangani, & Darwish, 2016). The + is defined inthe wall boundaries as,

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= (19)

Where, the normal distance to the wall, is thekinematic viscosity and is the friction velocity interms of the wall sheer stress.

Free Surface RegionIn marine CFD simulations, researchers

usually have to deal with the free surface betweenwater and air. For the case of the flooding simulationof a ship after damage in calm water, a low level ofmesh refinement is adequate to capture thedeformation of the free surface in the vicinity of thehull and the underlying velocity gradients. Thought,the volumetric discretisation of the region of the freesurface is more critical in the case of theinvestigation of the motions of the ship in waves. Inthe case in which the wave propagation is solvedwith the Navier-Stokes equations incorporating theVoF method for interface capturing, the refinementof the free surface cells should be increasedotherwise deformation of the wave characteristicsmay occur (ITTC, 2011). On the other hand, if thenumber of cells is increased too much, thecomputational penalty could significantly high. Forthe avoidance of these effects, it is advisable to use80 up 160 cells per wave length with an aspect ratioadjusted to the wave steepness (Peric, 2018).

Figure 5: Mesh discretization for the simulation of wavepropagation (Roenby, Larsen, Bredmose, & Jasak, 2017).

Pimple Algorithm in OpenFOAMThe challenge in the solution of Navier-Stokes

equations is the coupled pressure momentumsystem. The selection of the solution algorithm hashigh influence to the computational time of thesimulation, and it should be chosen based on thenature of the problem under investigation.

As the simulation of flooding of the damagedship is a time-marching problem and timediscretisation is introduced the choice of anappropriate time step. The time discretisation isrestricted by the Courant-Friendrichs-Lewy numberdefined as (Ferziger & Peric, 2002),

=∆

∆(20)

Where, is the magnitude of the velocity, ∆ is thetime step and ∆ is the length internval whichrepresents the length of the cell.

The solution algorithms which are underinvestigation for the time domain simulation of aship after damage are PISO (Pressure Implicit withSplitting of Operator) and PIMPLE (ImplicitPressure Method for Pressure-Linked Equations).Both the algorithms are iterative solvers for transientsimulations. PISO algorithm is suitable for CFLnumber below one. On the other hand, the PIMPLEalgorithm is a combination of SIMPLE (Semi-Implicit Method for Pressure-Linked Equations)used for steady state problems and PISO(Moukalled, Mangani, & Darwish, 2016). PIMPLEalgorithm is more flexible as it can be stable for CFLnumbers bigger than one. Furthermore, it providesthe opportunity for adjustment of the iterativeprocedure between convergence (speed) andstability (Holzmann, 2018; Foundation, 2014).

Figure 6: PIMPLE solution algorithm implemented inOpenFOAM (Aguerre, Damian, Gimenez, & Nigro,2013).

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6. BENCHMARKINGA benchmark case is presented in the following

section. The vessel in consideration is examinedwith time-domain simulation of flooding for a rangeof KG values. Following this, flooding simulationwith CFD is performed.

The ship under investigation is a combat vesselwith general particulars as presented in the followingtable. The damage condition under investigation is afour-compartment damage with the opening in thestarboard side of the ship. The compartments R1, R2are extended from port to starboard, and the twodouble bottom compartments from the centre linesymmetry plane to starboard side. For demonstrationpurposes, the investigation is performed for fourhypothetical KG values, 5.8 m, 6.71 m, 7.13 m , and8.0 m respectively.

Table 1: Main Particulars of the vessel.

Main Particulars – Full scaleLBP 141.8 m Δmld 8684 tBmld 20.6 m LCG1 -0.65 mTmld 7.49 m KGmld 7.84 m

Volumes of the CompartmentsDB1 143.4 m3 R1 1,266.3 m3

DB2 165.9 m3 R2 1,650.9 m3

Figure 7: Profile view of the hull.

Figure 8: The four damaged compartments of the case underinvestigation.

1 The Longitudinal reference point is locatedamidships.

Figure 9: Midship section presenting the DB1, R1compartments.

Static Stability The first step in the stability assessment for thespecific damage case is the calculation of the curveof static stability, GZ. For the calculation of therighting arm the method of lost buoyancy has beenused.

Figure 10: Curves of static stability for the four KG values.

Time-Domain SimulationsFor the four cases under investigation time-

domain simulation of flooding after damage hasbeen performed. The tool, which has been used isPROTEUS3 and the results are presenting in thefollowing graphs.

Figure 11: Roll response of the vessel for KG 5.8 m & 6.71m.

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Figure 12: Roll response of the vessel for KG 7.13 m & 8.0m.

The roll response follows the same pattern for allthe cases. As the KG value increases the impact offlooding in the transient response of the vesselincreases.

Verification with CFDFor CFD analysis, the OpenFOAM v1812 is

used. The overInterDyMFoam solver is used for twoincompressible, isothermal fluids with VOFinterface capturing approach, incorporating optionaloverset mesh motion (Foundation, 2014). The forcesand the moments on the hull are calculated with thecoupling of sixDoFRigidBodyMotion library, whichis provided with the package.

The CFD simulations have been performed inthe Archie – WeSt High Performance ComputingFacilities located at the University of Strathclyde.For each simulation 20 cores of Intel Xeon Gold6138 have been used with frequency 2.0 GHz and4.8 GB RAM per core.

Pre-ProcessingThe pre-processing steps involve the preparation

of the geometrical model and the generation of thegrids, which will be used. The problem domainincorporates two main regions. The first is a cylinderwith radius 2B, which includes the fluid domain inthe vicinity of the hull and the four internalcompartments of the ship. The second domainrepresents the earth-fixed environment in which theship is moving and is used for the interpolation of thefluid variables from and to the overset region.

Figure 13: 3D representation of the hull.

Figure 14: The overset region which encompass the hall andthe internal arrangement.

For grid generation, the ANSA v19.0.1 softwarehas been used, developed by the BETA CAE. For thecylindrical volume of the overset region, the gridelements, which have been chosen are tetrahedral fortwo main reasons. The first is their ability to captureeasier the geometry of the hull, and the edges insidethe ship arrangement. Furthermore, unstructuredtetrahedral elements provide the advantage of asmoother transition between the areas and volumeswith different cell size. The smooth transition of thevolumetric regions are crucial for the accuratevelocity and pressure gradients and the stability ofthe solver.

Figure 15: Transverse view of free surface, hull, and internalrefinement regions.

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Figure 16: The grid of the overset region.

The total number of cells of the overset regionare presented in the following table.

Table 2: Mesh sizes.

RegionsMesh Overset Background

Coarse 1,158,782 623,563Medium 1,881,975 173,911

Fine 4,338,449 623,563

Figure 17: Fine mesh discretization close to the bulbous bow.

The background domain is a rectangular regiondeveloped only with hexahedral elements locallyrefined close to the free surface and the oversetregion where the interpolation of the fluid variablesis performed.

Figure 18: The problem domain with the background andthe overset mesh regions.

Simulation Set-UpThe set-up of the simulation has been chosen

based on the demand of adequate accuracy andreasonable computational cost. For this reason thenumerical tank uses the PIMPLE algorithm, which

allows large time steps without jeopardizing thestability of the calculation (Holzmann, 2018;Foundation, 2014). In the simulations, the time stepcontrol is based on the maximum CFL number in thedomain and in the free-surface interface. Courantnumbers have been chosen as

< 25 & free surface < 5 (22)For the control of PIMPLE the tolerance of the

velocity and pressure fields have been set to thevalues of 10 and 10 , respectively. This is aconservative option as the aim was the stability ofthe simulation.

A very interesting and important topic in theCFD field is the selection of the appropriateturbulence model for the engineering problem underinvestigation. For this study, the kOmegaSST modelhas been chosen as it is the safest option for this kindof hydrodynamic problems (ITTC, 2011). For thecapturing of the viscosity near the wall boundaries,the default wall faction which in provided for theCFD toolkit is implemented.

The results for the simulation of medium meshin comparison with the results of the time-domainsimulation for KG =7.13m are presented in thefollowing figures.

Figure 4: A screenshot of the flooding at 4.0 sec.

Figure 20: Comparison between time-domain simulationand CFD.

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The results obtained demonstrate the impact offloodwater dynamics in the roll response of thevessel. Initially, from 0.0 up to 4.0 seconds the shiprolls to the side of the damage with a maximum rollangle approximately 4 degrees, two degrees belowthe roll angle that the time domain simulationpredicts. This phase is characterised by the motionof floodwater water front, resembling a dam-breakphenomenon. From 4.5 sec, the roll angle starts todecrease and at 10 sec the vessel rolls to the port sidewith a maximum angle approximately -4.0 degrees.This stage is defined by the large hydrodynamicimpact induced by the momentum of the floodwaterto the port side of the hull. After the first 10 sec thesynchronisation of the sloshing of the water insidethe compartments and the motion of the hullproduces a roll angle close to 10 degrees, the worstof the flooding scenario. After the initial transientstage the roll oscillation is decreased smoothly dueto the damping of the motion of the hull. A veryinteresting outcome of the stationary stage is thesmooth roll decade of the damaged hull.

In the figure, the roll response of the vessel asit has been calculated by CFD is presented. Theagreement of the medium (2 m cells) and fine (4 mcells) mesh is notable. Furthermore, the coarse meshcalculates a maximum roll angle lower byapproximately 3.5 degrees. The difference should beoccurred due to the coarse background mesh and itsimpact in the interpolation of the flow variables withthe overset region.

Figure 21: Mesh convergence analysis.

In terms of computational cost it has beennoticed that the most important factor is the time stepin each stage of the simulation. In the transient stagewhere the bigger CFL number is the waterfront ofthe floodwater the time step has a value close to0.001. After the dam break phenomenon when thewater touches the port side wall and up to themoment where the water reaches the maximum level

inside the compartment the maximum time step isapproximately 0.005. In the steady stationary state,with maximum CFL limit 25, the time step increasesto a value of 0.015. The optimized choice of time andspace discretization is most vital factor for thereduction of the computational cost of thesimulations.

7. CONCLUTIONSThis work presented the utilisation of CFD for

the assessment of the survivability of a ship afterdamage. Despite the big computational cost relatedwith high fidelity numerical simulations, it is proventhat they can be an important tool in naval architect’sarsenal for the investigation of flooding of ship afterdamage. Time-domain simulation based on CFD cancapture important phenomena that fast time-domaintools, based on hydraulic assumptions cannot, in alevel of detail that sometimes is important. Thediscrepancies that have been between DTNS andCFD are under investigation. Furthermore, theselection of the time and space discretization is a keyfactor and it needs more research.

8. ACKNOWLEDGMENTSThe authors of this paper would like to express

their gratitude to the sponsors of the Maritime SafetyResearch Centre, Royal Caribbean International &DNV – GL for their courtesy to support the researchendeavours of the centre. Results were obtainedusing the ARCHIE-WeSt High PerformanceComputer (www.archie-west.ac.uk) based at theUniversity of Strathclyde. Spacial thanks to theBETA CAE Systems (www.beta-cae.com) whichsupported this research work with for the provisionof the advance pre - processing platform ANSAv19.0.1.REFERENCESAguerre, H. J., Damian, S. M., Gimenez, J. M., & Nigro, N. M.

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