Impact Related Wave Loads

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Thomas E. Schelline-mail: [email protected]

Ould el Moctar

Germanischer Lloyd AG,Vorsetzen 35,

Hamburg 20459, Germany

Numerical Prediction ofImpact-Related Wave Loads onShipsWe present a numerical procedure to predict impact-related wave-induced (slamming)loads on ships. The procedure was applied to predict slamming loads on two ships thatfeature a flared bow with a pronounced bulb, hull shapes typical of modern offshoresupply vessels. The procedure used a chain of seakeeping codes. First, a linear Greenfunction panel code computed ship responses in unit amplitude regular waves. Shipspeed, wave frequency, and wave heading were systematically varied to cover all possiblecombinations likely to cause slamming. Regular design waves were selected on the basisof maximum magnitudes of relative normal velocity between ship critical areas and wave,averaged over the critical areas. Second, a nonlinear strip theory seakeeping code de-termined ship motions under design wave conditions, thereby accounting for the nonlin-ear pressure distribution up to the wave contour and the frequency dependence of theradiation forces (memory effect). Third, these nonlinearly computed ship motions consti-tuted part of the input for a Reynolds-averaged Navier–Stokes equations code that wasused to obtain slamming loads. Favorable comparison with available model test datavalidated the procedure and demonstrated its capability to predict slamming loads suit-able for design of ship structures. �DOI: 10.1115/1.2429695�

Keywords: wave impact, slamming loads, seakeeping codes, RANSE solver, ships

ntroductionWave-impact related �slamming� loads can induce high stresses

nd cause deformation of local structural components. The accu-ate assessment of such loads is essential for the design of a ship’structure. Classification society rules contain formulas for slam-ing loads, see e.g., Ref. �1�. Generally, these formulas are ad-

quate for conventional ships, as they are based on operationalxperience. However, for many modern ships it becomes neces-ary to resort to direct computations of slamming loads.

A satisfactory theoretical treatment of slamming has been pre-ented so far by the complexity of the problem. Most theories andheir numerical procedures were applied on two-dimensional bod-es; however, slamming is a strongly three-dimensional nonlinearhenomenon that is sensitive to the relative motion between thehip and the water surface �2�. Slamming is characterized byighly peaked local pressures of short duration. Hence, slammingeak pressures cannot be applied on larger areas to estimate struc-ural response to slamming impacts. Moreover, the influence ofydroelasticity, compressibility of water, and air pockets mayave to be accounted for. Mainly because of these phenomena,otential flow methods are not well suited to accurately predictlamming loads �3�. However, recent progress has been made inhe development of numerical methods that predict slammingressures �4�. Kinoshita et al. �5�, for example, predicted shipotions and loads with a Navier–Stokes solver. Although no ex-

reme load cases were presented, the applied method has the po-ential to compute slamming loads in extreme wave conditions.

A number of research projects during the recent past were ini-iated to develop numerical techniques that reliably predict slam-

ing loads on ships. Within the framework of the European re-earch project DEXTREMEL �6�, slamming loads on the bow

Contributed by the Ocean Offshore and Arctic Engineering Division of ASME forublication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manu-cript received June 26, 2006; final manuscript received November 8, 2006. Reviewonducted by Antonio C. Fernandes. Paper presented at the 25th International Con-erence on Offshore Mechanics and Arctic Engineering �OMAE2006�, Hamburg,
ermany, June 4–9, 2006.
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door of a generic RoRo Ferry design were investigated. To predictbow door loads on this ferry, Sames et al. �7� applied two methodsthat both start with linear seakeeping predictions of ship motions.Their first procedure, using a finite volume code, relies on com-puted impact pressure coefficients obtained from two-dimensionalwater entry simulations of vertical bow sections. Their secondprocedure, using a boundary element code, comprises two-dimensional water entry simulations of tilted bow sections. Com-parison with model test measurements showed that neither methodis capable of accurate predictions although the two methods areable to define upper and lower bounds.

Methods that directly solve the Reynolds-averaged Navier–Stokes equations �RANSE�, possibly including the two-phase flowof water and air, are better able to describe the physics associatedwith slamming. However, the computational effort for a three-dimensional RANSE method to simulate motions and loads on aship at small, successive instances of time over a long time periodappears beyond current computational capabilities. This paperpresents a recently developed numerical procedure �8� to predictslamming loads. The procedure consists of first making use of thetwo potential flow seakeeping codes GLPANEL �9,10� andGLSIMBEL �11�. GLPANEL selects the design waves, andGLSIMBEL determines the corresponding ship motions underthese �large amplitude� design wave conditions. The resulting shipmotions then serve as part of the input for the RANSE solverCOMET �12� to yield slamming loads.

The procedure was applied to predict slamming loads for tworeference ships, designated Hull 1 and Hull 2. Both ships feature aflared bow with a pronounced bulb and a flat overhanging stern,hull shapes typical of modern offshore supply vessels. Table 1lists principal particulars. Slamming loads were examined at theships’ forefoot. Specifically, areas under the flared bow were con-sidered. Model test measurements for one of the ships were avail-able for comparison with computations. The favorable agreement
validated this method.
FEBRUARY 2007, Vol. 129 / 3907 by ASME

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omputational ProcedureThe objective was to obtain spatial mean slamming pressures

hat can be applied as equivalent static design loads to determinecantlings of hull structural elements for the forebody of the twoeference ships. This was accomplished by integrating computedocal slamming pressures over selected critical areas of the hull.or these ships with flared bows, the area under the bow flareven when there is no keel emergence is generally subject tolamming. The following steps comprised the computationalethod:

1. The linear, frequency-domain Green-function panel codeGLPANEL computed ship responses in unit amplitude regu-lar waves. Wave frequency and wave heading were system-atically varied to cover all possible combinations that arelikely to cause slamming. Results were then linearly ex-trapolated to obtain responses in wave heights that representsevere conditions, here characterized by steep waves close tobreaking. Under such conditions, the added resistance tendsto result in voluntary or involuntary speed loss. Thus, theships were assumed advancing at reduced speeds.

2. Regular design waves were selected on the basis of maxi-mum magnitudes of relative normal velocity between shipcritical areas and wave averaged over these critical areas.This velocity is defined as follows

�n =

�i

�A� n�i · �� i

�i

��A� n�i��1�

where �A� n�i is the area vector normal to a surface patch i onthe ship’s hull defined by the computational grid generatedfor the GLPANEL computations; �� i is the relative velocity at

this patch i; and �i��A� n�i� is the examined critical area madeup of i surface patches.

3. The nonlinear strip method GLSIMBEL determined motionsof the ships under regular design wave conditions, therebyaccounting for the nonlinear pressure distribution up to thewave contour and the frequency dependence of the radiationforces �memory effect�.

4. The nonlinearly computed ship motions constituted part ofthe input for the RANSE code. To compute slamming loads,numerical volume grids surrounding the ships were gener-ated, appropriate boundary conditions were applied, andconvergence criteria were defined.

he Linear Panel MethodThe linear, frequency domain seakeeping panel code

LPANEL uses a zero-speed Green function and a forward speedorrection based on the encounter frequency approach. A velocityotential is found by distributing singularities over the mean wet-ed surface. Their strengths are determined by satisfying appropri-te boundary conditions, leading to integral equations for the sin-ularities. The integral equations are solved numerically byeplacing them with a set of linear equations, yielding the

Table 1 Principal particulars of the reference ships

Hull 1 Hull 2

ength between perpendiculars 70 m 130 molded breadth 15 m 20 mraft 5 m 6 misplacement 1550 t 5470 tervice speed 16 kn 18 knroude number 0.31 0.26

trengths of the singularities situated on a finite number of surface

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patches �panels� that discretize the wetted hull. Pressures are ob-tained according to the linearized Bernoulli equation. Integratingpressures over the hull surface results in hydrodynamic forces andmoments. Solving the motion equations yields ship motions.

The Nonlinear Strip MethodThe nonlinear strip theory seakeeping code GLSIMBEL simu-

lates large-amplitude rigid-body motions of a ship in six degreesof freedom by time-domain integration of the motion equations.Considered are forces and moments caused by gravity, Froude–Krylov pressure, radiation and diffraction pressure, speed effects,and rudder and propeller actions. Forces and moments caused byradiation and diffraction are deduced from the two-dimensionalpotential flow at each of the transverse ship sections �strips�.

The Froude–Krylov forces, resulting from the water pressureinduced by the incident waves, are integrated up to the wavecontour. In this way, these pressures also cause changes in therighting arm curve due to the changing position of the wave crestrelative to the ship. The waves themselves, however, are treatedlinearly according to Airy theory, which means that nonlinear ef-fects in steep seaways, such as higher and steeper wave crests thanwave troughs, are neglected.

Hydrodynamic radiation forces �added mass and damping� aregenerated by ship motions, whereas diffraction forces arise fromthe difference between the forces acting on the stationary ship inwaves and the Froude–Krylov forces. This difference is caused bythe change of the wave pressure field due to the presence of thestationary ship. For instance, if the ship partly emerges from thewater, the diffraction component of the emerged part must be zeroand thus cannot be computed for the nonmoving ship. Therefore,the computation of the sum of radiation and diffraction forces isbased on the relative motion hypothesis, that is, by assuming thatthe orbital velocity of the wave motion averaged over a ship crosssection determines the fluid force at that cross section. Summingthe contributions from all ship sections �strips� yields the totalforce on the ship. Longitudinal interactions due to forward speedeffects are treated in the same way as for linear strip methods.

The hydrodynamic pressure distribution depends not only onthe ship’s momentary position, velocity, and acceleration, but alsoon the past history of the ship’s motion, which is reflected in thewave pattern. In frequency domain computations, this so-calledmemory effect is expressed in the frequency dependence of addedmasses and damping. In time domain simulations, one solution isto use impulse-response functions by formulating the hydrody-

namic memory forces �and moments�, F� , as convolution integralsthat account for the dependency of these forces on the accelera-tions at different time steps

F� �t� =�−�

t

K��u��d� �2�

where the matrix K�� is determined from potential flow compu-tations of the individual strips at different immersion drafts andinclination angles of the waterline. The velocity u� contains notonly ship motions, but also the incident wave particle velocities.The waves are generated by the ship at time �t−��. As they arestill present at time t, they will continue to exert forces and mo-ments on the ship.

Although time domain simulations of ship response can be car-ried out with memory effects being updated at each time step byrecalculating all convolution integrals, it is numerically far moreefficient to use a finite state space approximation as advocated bySchmiechen �13�. The code makes use of this alternative. Insteadof relying on the proportionality between force and acceleration, arelation is established between acceleration and a few of its timederivatives on the one hand and of the force and a few of its time
derivatives on the other hand
Transactions of the ASME


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A0u + A1�

�tu + A2

�2

�t2 u + ¯ = B0 + B1 f + B2 f + ¯ �3�

here f is the force per unit length; and u is the acceleration. Bothf and u are three-component column vectors. Matrices A0, A1,

2 ,… and B0, B1, B2 , . . . are 3�3 complex matrices that do notepend on frequency, but they still depend on section shape, sub-ergence depth, and heel, and thus implicitly on time. They are

omputed from the frequency dependent added mass and dampingoefficients by regression analysis. Three degrees of freedom haveo be considered for each strip, namely, the transverse and verticalranslations and the roll motion. Thus, to enhance the numericalfficiency of simulations, these matrices are determined for a suf-cient number of �encounter� frequencies, immersion drafts, and

nclination angles before starting the simulations. During a simu-ation, values for the actual immersion and waterline inclinationre obtained by interpolation.

Terms account for effects of viscous hull damping in roll, usingroude number dependent coefficients. The influence of bilgeeels is approximated semi-empirically. Propeller thrust is consid-red, whereby a motion equation for the propulsion system deter-ines the propeller rate of rotation. Rudder forces and moments

re determined by considering the orbital motion of water par-icles and the immersion of the rudder in the seaway.

he RANSE SolverThe RANSE solver of COMET, a code that employs interface-

apturing techniques of the volume-of-fluid �VOF� type, was anbvious choice for computing complex freesurface shapes withreaking waves, sprays, and air trapping, hydrodynamic phenom-na that should be considered to predict slamming pressures.

In this code, the conservation equations for mass and momen-um in their integral form serve as the starting point. The solutionomain is subdivided into a finite number of control volumes thatay be of arbitrary shape. The integrals are numerically approxi-ated using the midpoint rule. The mass flux through each cell

ace is taken from the previous iteration, following a simple Pi-ard iteration approach. The remaining unknown variables at theenter of the cell face are determined by combining a centralifferencing scheme �CDS� with an upwind differencing schemeUDS� for the convective terms. The diffusive terms are dis-retized using CDS. The CDS employs a correction to ensureecond-order accuracy for an arbitrary cell. A second-order CDSan lead to unrealistic oscillations if the Péclet number exceedswo and large gradients are involved. On the other hand, an UDSs unconditionally stable, but leads to higher numerical diffusion.o obtain a good compromise between accuracy and stability, thechemes are blended.

Near the ship hull, the blending factor is chosen between 0.8nd 0.9. The three time level methods are used to integrate inime. Pressure and velocity are coupled by a variant of theIMPLE algorithm �14�. All equations except the pressure correc-

ion equations are under-relaxed using a relaxation factor of 0.8.he pressure correction equation is under-relaxed using a relax-tion factor between 0.2 and 0.4 for unsteady simulations, findingn each case a suitable compromise between stability and conver-ence speed.

The two-fluid system is modeled by a two-phase formulation ofhe governing equations. No explicit free surface is defined duringhe computations, and overturning �breaking� waves as well asuoyancy effects of trapped air are accounted for. The spatialistribution of each of the two fluids is obtained by solving andditional transport equation for the volume fraction of one of theuids. To accurately simulate the convective transport of the two

mmiscible fluids, the discretization must be nearly free of nu-erical diffusion and must not violate the boundedness criterion

14�. For this purpose, the high resolution interface capturingHRIC� scheme is used �15�. This scheme is a nonlinear blend of
pwind and downwind discretization, and the blending is a func-
ournal of Offshore Mechanics and Arctic Engineering


tion of the distribution of the volume fraction and the local Cou-rant number. The free surface is smeared over two to three controlvolumes. Fluid structure interaction effects are presently not ac-counted for, i.e., the body is assumed to be rigid. The fluid isassumed to be viscous and incompressible.

Flow SimulationThe numerical volume grids surrounding the ships comprised

about 1 1/2 million hexahedral control volumes. To avoid flowdisturbances at outer grid boundaries, these boundaries were lo-cated at a distance of one ship length ahead of the bow, two shiplengths aft of the stern, one ship length beneath the keel, and oneship length above the deck. The large domain of the mesh, espe-cially below the keel and above the deck, was chosen to allowlarge pitch motions in head waves. Near the ship hull and ahead ofthe ship, grid density was high to resolve the wave, whereas aft ofthe ship the grid became course to dampen the waves. The inner-most dimensionless cell thickness was chosen such that n+=100on average �15�. Figure 1 shows part of the numerical grid do-mains surrounding Hull 1.

Front, side, bottom, and top flow boundaries were specified asinlets of known velocities and known void fraction distributionsdefining water and air regions. On the hull surface a no-slip con-dition was enforced on fluid velocities and on the turbulent kineticenergy. The wake flow boundary was specified as a zero-gradientpressure boundary �hydrostatic pressure�. All computations wereperformed using the RNG-k-� turbulence model with wall func-tions �16�. The time step size was chosen such that the Courantnumber was smaller than unity on average. The momentum equa-tions were discretized using 85% central differences and 15% up-wind differences. Ship motions were realized by moving the entiregrid at each time step. Thus, all boundary conditions were newlycomputed at each time step.

Volume fractions and velocities that initialized the flow fieldarose from superposition of ship speed and orbital particle veloci-ties of the design waves. The influence of numerical damping onthe wave height was taken into account. Numerical diffusioncaused by the course grid aft of the ships dampened the incidentwave to such an extent that no significant wave reflection occurredat the outlet boundary.

For runs in regular waves, simulation of the flow field contin-ued until a periodic solution was reached. After a simulation timeof 2–5 encounter periods, depending on ship motions, ship speed,wave height, and position of the investigated plate fields, periodi-cally converging solutions were obtained. For each time step up to15 outer iterations were needed.

An earlier study �8� systematically investigated errors associ-ated with the use of different schemes to discretize the momentumequations. Slamming pressures as well as vertical forces on thehull were examined. It was found that the use of higher orderapproximation schemes increases the accuracy of pressure predic-tions; however, at the cost of encountering numerical instabilities.We chose an 85% CDS approximation as this was a reasonablecompromise between accuracy and numerical stability. This ear-lier study also found that the influence of the approximation

Fig. 1 Part of numerical grid domains surrounding Hull 1

scheme on vertical force predictions is almost insignificant.

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odel TestsThe Hamburg Ship Model Basin �HSVA� conducted systematic

eakeeping model tests of Hull 1 to experimentally validate theomputations. The self-propelled model, constructed at a scale of:10, was fitted with fixed stabilizing fins, twin shafts and propel-ers, and a set of steerable twin rudders. To obtain model test

easurements of hydrodynamic loads acting on the bow, a fore-ody hull segment was separated from the wooden model. Lo-ated above the stillwater line, this separated segment was con-ected to the ship model by a special force balance that enabledeasuring six-degree-of-freedom forces and moments acting on

his segment. The vertical separation of this hull segment wasocated 4.0 m aft of the forward perpendicular �at building frame0�; the lower and upper horizontal separations were situated.7 m and 7.2 m above the base line, respectively. The segment’surface area amounted to 53 m2. Global loads as well as localressures acting on the separated hull segment were measured.

Fig. 2 Computed and measured amplitudes„m/s2

… of Hull 1 in regular head waves

ocal pressures were recorded by two pressure sensors located at



a height of 5.2 m above the base line on each side of this hullsegment, with the port one positioned 2.0 m aft and the starboardon 0.5 m aft of the forward perpendicular. �All the given datarefer to full-scale values.� Measured loads on the separated bowsection were corrected for inertial effects.

During seakeeping tests, a gyro unit recorded pitch motions.Three accelerometers located at the aft perpendicular, at the posi-tion of the separated bow segment, and at the forward perpendicu-lar recorded vertical accelerations. Three wave probes located atthe aft perpendicular, at the longitudinal position of the pressuretransducers, and at the ship’s bow recorded ship motions relativeto the wave elevation.

The free-running model was hand operated by the helmsmanaccommodated on the carriage of HSVA’s large towing tank. Atotal of eight tests were run in regular head waves: Tests 1, 2, 3, 4,7, and 8 in waves of 2.0 m height and Test 5 and 6 in waves of3.5 m height. The wave length to ship length ratios ranged from

„a… pitch „deg… and „b… vertical acceleration
of
0.8 to 1.4, and the propeller turning rates corresponded to calm



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ater speeds of 14 kn for Tests 1 to 6 and to 16 kn for Tests 7 and. As head waves were investigated, only pitch and heave motionsere considered.Computed GLPANEL results generally compared favorably

ith measurements, which was expected because the waveeights were relatively small during the model tests. Figure 2hows amplitudes of pitch motion and vertical acceleration at theorward perpendicular for all eight test cases. Here the dark barsdentify computed results; the light bars, measured results. Posi-ive as well as negative values are depicted. They relate to a right-anded coordinate system, fixed with respect to the mean positionf the ship and translating in the positive x direction. The y axis isositive to port; the z axis, positive upward. Measured valuesepresent steady state conditions.

The location of the separated bow section and the critical plateelds 1 and 2 are shown in Fig. 3. Under the HSVA test condi-

ions, the RANSE solver performed computations of wave-nduced slamming loads and local pressures acting on the sepa-ated bow section of the ship. Simulations of the flow field wereerformed over two consecutive encounter periods, while mea-urements lasted over several periods. Over the first two periods,he computed vertical force on the separated bow compared favor-bly with measurements �Fig. 4�. For the corresponding slammingressures, averaged over the plate field areas, the functional rela-ionship of computed values compared favorably with experimen-al data, but peak values differed. This deviation was largely at-ributed to the relatively strong variation of the measured peaks,

ost likely caused by the inability of the model to attain steadytate conditions during tests in regular waves. At both plate fields,he time histories of measured and computed pressures were simi-ar. In Fig. 5 these histories are shown for plate field 1.

The force and pressure histories in Figs. 4 and 5 are presenteds nondimensional values. Force �FV� was normalized by a maxi-

ig. 3 Locations of separated bow section „dark shading… andritical plate fields „light shading… for Hull 1

ig. 4 Time histories of measured and computed vertical force
n bow section of Hull 1


mum value of F0=2350 kN; pressure �psl�, by a maximum valueof p0=265 kPa; and time �Time�, by the wave encounter period ofT0=6.0 s.

Design Wave ConditionsFor both ships, only head wave conditions were investigated

because these conditions were rated most critical from the stand-point of slamming loads on the forebody. Based on the systematicGLPANEL computations, performed for five different ship speedsand 30 different wave frequencies, equivalent regular designwaves were selected according to the following three limiting cri-teria:

• The vertical acceleration on the bridge may not exceed 1.0g�g=acceleration of gravity�;

• The propeller tips may not emerge from the sea surface�avoid propeller racing�; and

• The wave height may not exceed one-tenth of the wavelength �consider only nonbreaking waves�.

We examined all waves that met these criteria and selecteddesign wave conditions on the basis of the largest relative normalvelocity that was experienced at the center of each critical platefield at the time of slamming. In principle, this process yieldeddifferent design wave conditions for each plate field. However, thecritical plate fields under the flared bow of Hull 1 as well as underthe flared bow of Hull 2 were located closely together, and therelative normal velocities at these plate fields were nearly thesame. Therefore, we considered only one design wave conditionfor each hull. Table 2 summarizes the two design wave conditions.

Results for Hull 1The nonlinear GLSIMBEL computations provided ship motions

at design wave conditions. Since the response had an almost har-monic behavior in the frequency of the incident wave, we used

Fig. 5 Time histories of measured and computed pressureson plate field 1 of Hull 1

Table 2 Design wave conditions

Hull 1 Hull 2

Wave height 7.0 m 11.0 mWave length 112.8 m 120.6 mWave length / ship length 1.61 0.93Wave length / wave height 16.1 10.9Wave encounter period 5.8 s 6.0 sShip speed 12.1 kn 12.0 kn

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time harmonic functions to describe all motion characteristics.The corresponding heave and pitch amplitudes were 4.6 m and11.1 deg, respectively.

Four areas under the flared bow were considered critical for thestructural design of Hull 1, and the computed slamming pressureswere averaged over these areas. The locations of these areas areshown in Figs. 6 and 7, where they are identified as plate fieldsnumbered 1–4 having areas of 0.2 m2, 4.5 m2, 5.1 m2, and4.5 m2, respectively.

The three-dimensional flow field surrounding the hull under theinfluence of design wave conditions was computed as a transientprocess. Computed pressures hardly changed after the first period.Over the third period, computed time histories of these averagedslamming pressures are shown in Fig. 8. Short duration peak pres-sures are seen to be highest at plate fields 1 and 2, reaching peakvalues of about 180 kPa. A typical pressure distribution over theship’s hull, corresponding to the time of maximum pressure peakoccurrence, is shown in Fig. 9.

The corresponding design value according to classification so-ciety rules �1� is 105 kPa, which is significantly less than thecomputed value of 180 kPa. These two values are not directlycomparable, because, amongs others, a safety factor between thedesign �rule� value and the computed �extreme� value must beconsidered to account for the difference between the allowablestress and the yield stress of the material.

Fig. 8 Time histories of slamming pressures at plate fields 1–4for Hull 1

ig. 6 Locations of „a… critical plate field 1 and „b… critical plateeld 2 for Hull 1

ig. 7 Locations of „a… critical plate field 3 and „b… critical plateeld 4 for Hull 1

ribution during slamming for Hull 1



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esults for Hull 2Again, GLSIMBEL computations provided ship motions at de-

ign wave conditions, and the response also had an almost har-

Fig. 10 Locations of critical plate fields for Hull 2

Fig. 11 Simulation of Hull 2 under design wave condit



monic behavior in the frequency of the incident wave. Using timeharmonic functions to describe the motion characteristics yieldedheave and pitch amplitudes of 2.3 m and 6.8 deg, respectively.

For Hull 2, three areas under the flared bow were consideredcritical for structural design and, as for Hull 1, the computedslamming pressures were averaged over these areas. Their loca-tions, shown in Fig. 10, are indentified as plate fields numbered 1to 3 having areas of 7.7, 0.7, and 5.8 m2, respectively.

The three-dimensional flow field surrounding the hull under theinfluence of design wave conditions was computed as a transientprocess. As seen in Fig. 11, the ship’s bow emerged and the deckimmersed. The re-entry of the bow after emergence not only re-sulted in slamming under the ship’s bow flare, but it also causedwater to flow onto the deck. Figure 12 shows the correspondingpressure distribution, demonstrating that impactrelated slammingpressures occurred under the flared bow directly above the bulb.

Computed pressure histories acting at plate fields 1 and 3 areshown in Fig. 13. The nondimensional pressure �psl� is normalized

ions: „a… deck immergence and „b… bow emergence

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y the maximum value of p0=265 kPa; the nondimensional timeTime�, by the wave encounter period of T0=6.0 s. Pressures act-ng at plate field 2 were almost identical to pressures acting atlate field 1 and, therefore, are not plotted. Because of its locationhead of plate fields 2 and 3, plate field 1 experienced the highestressure peak of about 275 kPa. The peak pressure acting at plateeld 3 was only about 65% as high as the peak pressure acting atlate field 1.

The corresponding design value for Hull 2 according to classi-cation society rules �1� is 163 kPa. As for Hull 1, this value isignificantly less than the computed value of 275 kPa. Here again,he same reasoning applies also for Hull 2 in that these two valuesre not directly comparable, because, amongst others, a safetyactor between the design �rule� value and the computed �extreme�alue must be considered to account for the difference betweenhe allowable stress and the yield stress of the material.

iscussionAccurate prediction of slamming loads continues to be difficult,ainly because of the many parameters involved. The procedure

resented here attempted to combine the physics of a ship inaves with the use of advanced numerical techniques.

Fig. 12 Pressure

ig. 13 Time histories of slamming pressure for Hull 2 under
esign wave conditions


The generally favorable agreement between predicted slam-ming loads and comparable data from model test measurementswas mainly due to averaging the pressures over selected areas. Itwas this approach that made it possible to use the resulting slam-ming load predictions for design purposes.

The functional relationships of computed pressures corre-sponded to classical measured slamming pressures. Slamming oc-curred when the incident wave caused the plate fields to immerse.Pressures then suddenly increased to their peak values and de-creased rapidly afterwards to about on fifth of their peaks. Pres-sures then slowly decreased further until they reached atmosphericpressure.

We modeled the seaway by defining equivalent regular designwaves although such design waves only roughly approximate re-ality.

The influence of structural deformation was not accounted foralthough it does affect impact-related loads. Including this effectwould most likely have led to somewhat smaller local slammingloads.

ConclusionsComputed results of wave-induced slamming loads demon-

strated that the procedure presented here was capable of predict-ing slamming suitable for design of a ship’s structure. The gener-ally favorable comparison of computations with model testmeasurements validated the procedure.

Before using the RANSE solver, it was necessary to identifywave conditions likely to cause severe slamming and to obtainreliable predictions of ship motions under such conditions. There-fore, motions could not be predicted from linear methods alone. Asubsequent nonlinear analysis was necessary to yield sufficientlyaccurate motion predictions that were then used as part of theinput for the RANSE solver.

The RANSE code COMET is currently being modified to alsosolve the ship motion equations, so that in future it will not berequired to supply predetermined ship motions as part of the in-put.

References�1� Germanischer, L., 2005, “Rules for the Classification and Construction, I Ship

Technology, 1 Seagoing Ships, 1 Hull Structures,” Hamburg.�2� Tanizawa, K., and Bertram, V., 1998, Slamming, Handbuch der Werften Chap.

XXIV, Hansa-Verlag, Hamburg, Germany, pp. 191–210 �in German�.�3� Mansour, A. E., and Ertikin, R. C., eds., 2003, “ISSC: Technical Committee

I.2 LOADS,” Proceedings 15th International Ship and Offshore StructuresCongress, Vol. 1, San Diego, CA, August 11–15, pp. 87–90.

tribution on Hull 2
dis
�4� Ohtsubo, H., and Sumi, Y., eds., 2000, “ISSC: Technical Committee I.2



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LOADS,” Proceeding 14th International Ship and Offshore Structures Con-gress, Vol. 1, Nagasaki, Japan, pp. 102–107.

�5� Kinoshita, T., Kagemoto, H., and Fujino, M., 1999, “A CFD Application toWave-Induced Floating-Body Dynamics,” Proceedings International Confer-ence on Numerical Ship Hydrodynamics, Nantes, France.

�6� DEXTREMEL, 2001, “Design for Structural Safety Under Extreme Loads,”Brite Euram III Research Project, Contract No. BRPR-CT97-0513, Final Tech-nical Report at http://research.germanlloyd.org/Projects/DEXTREMEL/DEXTR.

�7� Sames, P. C., Kapsenberg, G. K., and Corrignan, P., 2001, “Prediction of BowDoor Loads in Extreme Wave Conditions,” Proceedings of the InternationalConference Design and Operation for Abnormal Conditions II, RINA, London,November 6–7.

�8� El Moctar, O., Brehm, A., and Schellin, T. E., 2004, “Prediction of SlammingLoads for Ship Structural Design Using Potential Flow and RANSE Codes,”Proceeding 25th Symposium on Naval Hydrodynamics, St. John’s, August8–13.

�9� Östergaard, C., and Schellin, T. E., 1995, “Development of an Hydrodynamic
Panel Method for Practical Analysis of Ships in a Seaway,” Trans. Schiffbau-


technische Gesellschaft, 89, pp. 561–576 �in German�.�10� Papanikolaou, A. D., and Schellin, T. E., 1992, “A Three-Dimensional Panel

Method for Motions and Loads of Ships with Forward Speed,” J. Ship Techn.Research 39, pp. 147–156.

�11� Pereira, R., 1988, “Simulation of Nonlinear Sea Loads,” J. Ship Techn. Re-search, 35, pp. 173–193.

�12� ICCM, 1998–2000, User Manuel COMET Version 2.0, Institute of Computa-tional Continuum Mechanics GmbH, Hamburg, Germany.

�13� Schmiechen, M., 1973, “On State Space Models and Their Application toHydrodynamic Systems,” Univ. of Tokyo, Dept. of Naval Arch., NAUT ReportNo. 5002.

�14� Ferziger, J., and Peric, M., 1996, Computational Methods for Fluid Dynamics,Springer, Berlin.

�15� Muzaferija, S., and Peric, M., 1998, “Computation of Free-Surface Flows Us-ing Interface-Tracking and Interface-Capturing-Methods,” Nonlinear WaterWave Interaction, Computational Mechanics Publ., Southampton, pp. 59–100.

�16� Speziale, C. G., and Thangam, S., 1992, “Analysis of an RNG Based Turbu-
lence Model for Separated Flows,” Int. J. Eng. Sci. 30, pp. 1379–1388.
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Impact Related Wave Loads