BOW FLARE SLAMMING OF CONTAINER SHIPS AND IT'S IMPACT ON OPERATIONAL RELIABILITY

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1 BOW FLARE SLAMMING OF CONTAINER SHIPS AND IT'S IMPACT ON OPERATIONAL RELIABILITY R P Dallinga, Maritime Research Institute Netherlands (MARIN), Wageningen, The Netherlands SUMMARY Because the numerical prediction of bow flare slamming and the related transient hull girder response are still out of reach, tests with a flexible model were performed to obtain an impression of the effects of wave condition, ship heading and speed The results are used to characterise the statistical character of the joint statistics of the rigid body and flexural response An empirical model for the magnitude of the whipping response was derived and used, with criteria for tolerable whipping response, in scenario simulations to quantify the effect of slamming on the operational reliability and the effects of slamming on the long-term distribution of the vertical accelerations INTRODUCTION There seems to be a widespread consensus on the notion that slamming in the bow area is a just reason for the master of a ship to slow down in waves At the same time there seems considerably less consensus on how the master exactly judges the severity of a given situation Structural damage to the shell plating and the structure of focsle, safety threats related to lashing problems with containers and the stowage of their content and a crew that feels uncomfortable with the transient character of the ship s behaviour seem to be relevant issues for a container ship Most of the research on wave-induced slamming focuses on the pressures and related impulsive loading Although relevant for damage to shell plating, this information hardly relates to the clues that the master has at his disposal to judge the risk of damage and lashing and stowage problems Because of this, and because the practical prediction of the pressures is still out of reach, the present work focuses on the slamming-induced hull girder deflections (the whipping response) instead The most important target of the present work was to obtain practical information on the effect of ship speed and heading and wave height on the statistical nature of the whipping response and the joint statistics of the rigid body and flexural response TEST CASE THE SHIP The :67 model represented a m fast container ship The flexural mode shapes in the vertical plane were mimicked in a relatively crude way by reducing the stiffness of the wooden model at 6 locations along the length The stiffness and weight distribution were selected such that the lowest deflection mode shape and the natural frequency mimicked the assumed -node deflection mode of the ship The natural frequency in this mode amounted to 85 Hz The obtained natural frequency in the 3-node response was 35 Hz Although transverse and torsional deflections might be important as well for a container ship, only the deflections in the vertical plane were considered in the present sample case During the tests the model was self-propelled at constant propeller rpm and steered by means of an autopilot This test procedure allows for the effect of natural speed variations on the impact loads Length L pp [m] Beam B wl [m] 66 Draught T [m] 87 Displacement Δ [Tf] 7 TrStab GM t [m] 5 NatPer Roll T φ [s] 75 Nat Period T- node [s] Bending f- node [Hz] 85 Table : Ship Particulars TEST PROGRAMME The tests were performed in the course of the DYLOPROPS project, a project that aims at a better and complete understanding of propeller loads in service conditions (a) Tests The over-all test programme comprised a range of 3 wave conditions from various directions at a number of speeds The present results were obtained during the tests in waves from forward directions Because of the exploratory nature of the investigation test duration was sacrificed to allow a larger parameter space Most tests lasted the equivalent of runs in the basin; in each run the model covers a distance of around 5 m, which corresponds with 5-3 miles prototype A consortium consisting of Wärtsilä Propulsion Netherlands, Delft University of Technology, Netherlands Defence Academy and MARIN

2 To obtain an accurate impression of the statistics, some tests were extended to considerable longer test duration All tests were performed in the MARIN Seakeeping and Manoeuvring Basin in long-crested irregular waves (b) Measurements The measurements comprised the ship motions, rudder and propeller loads and the vertical accelerations at the forward and aft end of each of the 6 model segments (the sections in between the points where the stiffness of the wooden hull was reduced) 3 ANALYSIS Considering the frequency contents of the accelerations one can distinguish a component that corresponds with the encounter frequency of the incident waves (denoted as the wave frequency (WF) or rigid body component) and a component that consists of higher frequencies (denoted as the high frequency (HF), whipping or flexural component) 3 (a) Joint statistics Although interesting in it self, the joint statistics of the rigid body and whipping response are governing practical consequences of slamming in terms of for instance lashing loads The effect was obtained with a search for the maxima in the total signal in the (time-wise) proximity of the maxima of the rigid body accelerations Figure shows the analysis procedure A conceptual advantage of the procedure is the fact that the problem of identifying the number of slam events is circumvented x atot x awf search range secondary signal primary signal 3 SLAMMING EVENTS Basically, the whipping component in the accelerations and bending moment may be understood as a slowly decaying vibration after a transient start (due to an impulsive excitation) In practice the identification of these events is not straightforward Higher-order excitation from other sources [6] and the cumulative effect of subsequent wave encounters make it difficult to distinguish the smaller slamming events See Figure Total Vert Acc Bow Figure : SLAM PEAK analysis 3 (b) Distributions and key statistics The derived local extremes and the difference between the total and rigid body response were sorted to obtain the cumulative frequency of exceedance Subsequently, the results were characterised in terms of the mean and the mean of the highest one-tenth and one-third fractions Joint Distribution Acc [m/s] Time [s] Whipping Component Vert Acc Bow Freq of Exceedance [-] Acc [m/s] Time [s] Figure : Sample Whipping Response (6 knots, BF, Head Seas) Amplitude [m/s] WF measured TOT measured Sorted Increase of WF Response Fitted Rayleigh Distrib WF part F vs sum sorted (azwf+azhf) Neg Exp based on Mean Figure 3: Cum Distrib of the Acc Components at the Bow (BF, Head Seas, 6 knots)

3 4 SPECTRAL CHARACTERISTICS Figure 4 shows the frequency content of the vertical accelerations at the bow, at St and at the stern as obtained from a test in head-on BF 8 at knots The -node and 3-node response peaks at 85 and 35 Hz are clearly recognized just as well as the wave frequency component around Hz Spectral Density [m/s4s] Spectra VAcc Bow BF 8, knots Encounter Freq [Hz] Bow ST Aft Figure 4: Spectra Vertical Accelerations Noteworthy is the fact that the acceleration response in the frequency range above the 3-node mode is not negligible This poses a dilemma in the analysis because on one hand it shows higher order response cannot be totally neglected (the effects on the extreme values is notable) On the other hand the high frequency response of the model is probably not representative for that of the ship because the mode shapes are not modelled explicitly All present results are derived on the basis of the frequency contents up to 3 Hz 5 STATISTICAL CHARACTERISTICS 5 DIRECT RESULTS FROM LONGER TESTS A limited number of tests with a longer duration were performed to obtain a good impression of the statistical character of the results The results of one of these tests, in a head-on BF at 6 knots with around 4 wave encounters, are shown in Figure 3 The frequency of exceedance (the fraction of the wave encounters) is plotted on a logarithmic scale Considering the rigid body wave frequency part of the response it shows that a Rayleigh distribution fits the distribution quite well The predicted frequency of exceedance F of an amplitude x a for a given rms σ x value of the signal x is given by: x a F(x x a ) = e σ The distribution of the difference between the total accelerations and the wave frequency part can be approximated with a negative exponential distribution determined by the mean amplitude μ xa given by: F(x ) = e a x μ a x a The distribution of the sum of the wave frequency and whipping components is estimated by adding amplitudes of the above distributions After some algebra the distribution follows as: xa σx σx xa σ (( + ) + x ) μ a μ μ a a μa μa F(x a ) = e The fact that the above fits the measurements quite well implies a high temporal coherence between the magnitudes of both contributing components This is not entirely trivial because steep waves with low rigid body accelerations lead to high slamming loads 5 KEY STATISTICS FROM SHORTER TESTS Also the tests of shorter duration were used to check the statistical character of the increase above the wave frequency acceleration component This was achieved by comparing the ratio of the mean of the highest / rd 3 and / th fractions over the mean value with their theoretical equivalents given by [7]: /B N x/ N = A[(ln(N) + Γ (,ln(n))] B B in which N represents the highest fraction under consideration, A the Weibull scale factor, B the Weibull shape factor and Γ the incomplete Gamma function If B takes the value of, the distribution corresponds with the well-known Rayleigh distribution B equal to yields a negative exponential distribution Comparing the Rayleigh and the negative exponential distribution it shows that the ratio of mean of the highest / 3 rd fraction over the mean equals for a negative exponential distribution and 57 for a Rayleigh distribution The fact that for the highest / th fraction the ratios are 33 and times the mean demonstrates that the difference in character will manifest itself in particular in the extreme values Weibul shape factor B Hi rd / 3 mean x a/3 /x a/ Hi / th / Hi /3 rd x a/ /x a/ Table : Effect of shape factor B on typical higher values

4 Figure 5 shows the magnitude of the mean of the highest / 3 rd and / th fractions of the increase above the wave frequency accelerations versus the mean value for all tests in waves from ahead and from the bow quarter The trends are compared with the character of a negative exponential distribution Despite the scatter in the results (also due to the limited test duration) the results suggest that the above fits the whipping induced increase in the vertical accelerations quite well A practical consequence of the above is that the effect can be characterised by a single parameter, the mean value Noteworthy is the fact that the above observation also holds for the isolated whipping component of the accelerations An analysis that derives one local maximum per wave encounter also yields results that show a negative exponential distribution The values are about twice as high as the above increase above the rigid body accelerations Encouraging is the fact that the nature of the increase in the acceleration levels is similar to the results of a recent measurement campaign at sea [] Mean /3rd, th [m/s ] Key Statistics of Whipping Addition Waves from Fwd Direction Mean [m/s ] Max VertAcc [m/s] Effect of Slamming on Vert Acceleration BF, Head Seas Longitudinal Pos [St] TOT+8 WF+8 TOT-8 WF-8 TOT+6 WF+6 TOT-6 WF-6 Figure 6: Effect Longitudinal Position on Rigid Body and Total Accelerations at 8 and 6 knots Although slamming yields an upward impulsive load it is interesting to note that the downward (negative) accelerations seem to be affected at least as much as the upward ones 6 EFFECT OF SHIP SPEED AND WAVE CONDITION A first attempt to cover the effects of forward speed and wave height and period follow Ochi s classical work on the severity of slamming in which he relates it to the vertical relative velocity at the bow [7] 5 Mean Whipping Incr VAcc St /3rd /th NExp /3rd NExp /th Figure 5: Key statistics in waves from forward directions 6 DRIVING PARAMETERS Mean WhAcc [m/s] 5 6 EFFECT OF ON-BOARD LONGITUDINAL POSITION Figure 6 shows the effects of the longitudinal position on the magnitude of the rigid body and total vertical accelerations Apart from the classical trend in the rigid body response, with the lowest values in the area behind midships, and the effect of whipping in the bow area it demonstrates that also the accelerations at the stern are affected by slamming A check on the nature of the distributions shows that its character largely resembles that of the whipping response in the bow area 3 Speed [knots] Ship Vel x Square RMS RelVelBow Square rms RelVel Measured 745 m Hs Ship Vel x Square RMS RelVel Square RMS RelVel Measured 485 m Hs Figure 7: Effect of Forward Speed

5 The dashed line in Figure 7 compares the trend in this estimate with the trend in the test results It shows a clear deviation The notion that through the change in momentum of the water that is deflected by the pitching bow, forward speed plays also a direct role, lead us to try a fit with the product of the forward speed and the square of the vertical relative velocity Although this parameter requires a more thorough theoretical base, it seems to give much better results The above discrepancy between the common way to assess slamming and the present results may also be related to the fact that pressure assessments neglect the effects of the exposure area (which drives the total excitation) and the duration of an impact which determines, together with the natural periods of the various mode shapes, which mode shapes are excited 63 HEADING AND WAVE STEEPNESS In-house (unpublished) results for a ferry in waves from various forward directions showed that the above observation is not limited to head seas Figure 8 indicates results obtained with a segmented ferry model at one speed in irregular waves from various directions Despite the large change in the physics of the excitation (with only the weather side contributing), waves from the bow quarter yield a slamming response that is very similar to head seas The important effect of wave steepness in the ferry data in Figure 8 indicates that this parameter cannot be neglected in an assessment of the whipping response Red VAcc [m/s /(m/s) ] Effect Heading and Wave Steepness Mean Hi /3rd Whipping AccBow / rms RelVel Heading [deg] Figure 8: Effect of Heading and Wave Steepness on the Whipping Accelerations at the Bow of a Ferry 7 CONSEQUENCES OF THE OBSERVATIONS Because of its character, the whipping response increases the ratio of the extreme and the typical amplitudes This point is illustrated in Table 3 for a one-hour exposure and a range of speeds in a head-on BF It may explain why heavy slams are often referred to as freak events Speed knots 8 6 Nowave enc rms RelVelocity m/s mean WhAcc ) m/s rms WF Acc m/s MPrWH Acc m/s MPrWF Acc m/s MPrTot Acc ) m/s Extr WF Acc m/s ExtrTotAcc 3) m/s ) : the increase of the WF component due to whipping ) : the most prob ext, exceeded by 63% of the exposed ships 3) : an extreme value exceeded by % of the exposed ships Table 3: Effect of the Whipping Acc on the Vert Acc at the Bow in BF, Head Seas 8 IMPACT ON THE OPERATIONAL PERFORMANCE 8 INTRODUCTION An increased bow flare increases the capacity of a container ship In the majority of cases where the weather is good this increases the revenues for the owner In the minority of cases with bad weather, the revenues decrease because of risk avoiding measures of the master (reducing speed or sailing around bad weather areas) and cost increase (because of the direct and indirect costs of incidental damage to cargo and ship) In practice the following elements play a role in this complex trade off: The wave climate on the operational route The accuracy of the weather forecast The accuracy of the subsequent assessment of the anticipated ship behaviour (in particular the components that are likely to cause damage, like roll, green water and combined accelerations) The seakeeping characteristics of the ship (bow flare, stern submergence, transverse stability, natural period of roll) The ability to recover weather delays (service margin) The structural response of the ship structure (in particular the response to impulsive loads, where the natural periods and also the damping in the global mode shapes are important) The structural capacity of the ship, the container lashings and the containers themselves The dynamic behaviour of the container tack and their contents under an impulsive load

6 An optimisation requires a trade-off of: The mean trip duration The irregularity of the trip duration The fuel consumption The insurance costs (which presumably depend on the damage record of a ship) The costs and delays due to the repair of incidental damage 8 SCENARIO SIMULATIONS AND THEIR ANALYSIS In an effort to account for some of the above aspects (in a schematic way) we simulated a large number of trans- Atlantic voyages on a fixed route with the GULLIVER code [4] Apart from the involuntary speed loss due to the added resistance from wind and waves prudent seamanship was accounted for For the sake of simplicity this was limited to a reactive speed reduction to reduce the vertical accelerations The minimum speed was determined by the medium power, which amounted to 3% MCR Proactive measures (like weather avoidance) and the effects of the weather forecast were neglected Just-in-Time scenarios were simulated for: Involuntary speed loss only A voluntary speed reduction (VSR) based on the rigid body accelerations The simulated cases covered calm water at the optimum speed and westbound trips The simulations cover a period of 5 years in which 3 west-bound trips are made in a total of 366 steps in hour on the 943 mile route The maximum power was limited to 95% MCR The weather input for the simulations consisted of operational data from the ECMWF [] database The average wave height on the route was m, the highest wave heights were around m significant wave height 83 ESTIMATE OF THE MEAN INCREASE OF THE VERTICAL ACCELERATIONS The mean value of the whipping induced increase of the amplitude in the vertical accelerations at the bow was estimated from the ship speed (in m/s), the relative vertical velocity at the bow (the rms in m/s) and an indicator for the wave steepness (H s /T p ) with: H s /Tp μ a = 5v s σ svbow 5 84 LONG-TERM DISTRIBUTIONS The results of the scenario simulations cover the various aspects of behaviour, speed and fuel consumption for every hourly step with index i in a crossing Among these are the mean whipping induced acceleration amplitude increase μ i, the rms of the rigid body accelerations σ i and the number of wave encounters n i Using the equations from section 5 this makes it possible to calculate the probability of exceeding particular acceleration level x a at each step i The probability of exceeding this amplitude once or more in the entire simulation equals: n ( ) i P Esim (x a ) = F(x a, μi, σi ) i The above represents the probability with a long-term exposure that covers the entire simulation period of around 5 years The probability per trip follows by considering the number of trips N simulated in that period n ( ) i P Etrip (x a ) = N F(x a, μi, σi ) i 83 (a) Results Figure 9 indicates the distribution of the trip maxima for the case without measures to avoid high acceleration levels It shows that in this rather extreme case the whipping response magnifies the trip maxima by about 5% Fraction of Trips [-] 3 Long-Term Distribution Trip Maxima Trip Maximum [m/s] Rigid Body Rigid Body+Slamming Figure 9: Long-term distributions without VSR Figure indicates the above distributions when accounting for a voluntary speed reduction It shows that the VSR is not a guarantee for low accelerations Regarding the rigid body accelerations one of the reasons is the rather large number of wave encounters in conditions close to the adopted criterion Regarding the total accelerations a reason is that the correlation between the rigid body and whipping component is limited

7 LT Distrib Trip Maxima The saturation at lower levels is due to the minmium power that is maintained (3% MCR) and the fact that the lower speed increases the number of wave encounters (which magnifies the risk of exceeding a high value) Fraction of Trips [-] Trip Maximum [m/s] RB A cc, no VSR RB A cc, max 7m/s SDA RB TotAcc, no VSR TotAcc, max 7m/s SDA RB Figure : Effect of VSR on Trip Maxima Again encouraging is the fact that the magnitude of the increase in the acceleration levels under a prudent seamanship scenario is similar (around 3%) to the results of long-term stress measurements at sea [] In the foregoing the rigid body accelerations were used by the virtual captain as a criterion to slow down The figure below shows the effects of a systematic variation % Trip Exc Trip Maximum [m/s] Effect of Tolerable Maximum Rigid Body Acceleration on Encontered Extreme Values VSR Criterion for Tolerable Rigid Body Acc at the Bow (SDA, m/s] Rigid Flex Figure : Effect of VSR criterion on trip maxima Adopting a more stringent criterion for the maximum vertical accelerations only works up to a certain level 84 ECONOMY The impact of slamming on the economic performance is estimated with a very simple economic model that assumes a fully flexible market and neglects cargohandling costs It follows Evans and Marlowe [5] by adopting an evaluation on the basis of the revenues and costs per unit of time Along these lines the profit is the difference between the hourly earnings (the freight rate FR (in $/unit of cargo) times the cargo carrying capacity C Cap divided by the time V Dur it takes to perform the trip) on one hand and the sum of the fixed costs per hour Fixed Costs and the variable costs Var Costs per hour on the other C Cap *FR Pr ofit = VarCosts FixedCosts V Dur At low ship speeds the voyage duration reduces the hourly revenues to a level where it does not cover the fixed costs At very high speeds the rapidly, progressively, increasing fuel consumption absorbs more than the revenues In general there is, of course, a range of speeds where the revenues exceed the total cost In the present example we adjusted the freight rate such that with contemporary fuel costs (5 $/Ton) the optimum speed was 4 knots The fixed costs were taken such that a profit of 4% of the turnover is obtained in calm water Figure shows the effects of the weather and the voluntary speed reduction on the profit and duration of individual trips It shows that the VSR has a notable impact on the reliability and economy FractionTurn-Over Effect of Slamming on Hourly Profit Calm Water w/o VSR VSR 5 m/s VSR 7 m/s Trip Duration [hrs] Figure : Profit and Trip Duration

8 The results of a variation of the criterion for a voluntary speed reduction on the over-all economy are shown in Figure 3 In this figure the difference between the optimum in calm water and the simulations without Voluntary Speed Reduction (VSR) reflects the impact of the added resistance from wind and waves For the present slender high-speed ship it is relatively low; it corresponds with about 4% of the turnover A voluntary speed reduction to avoid excessive accelerations has a mixed influence Down to 7 m/s the effect on the over-all economy (here the transport capacity) is quite limited The effect on the reliability is larger The importance that many ship owners give to reliability, stresses the need for a cost function that takes this factor into account If it becomes possible to value reliability in economic terms it becomes possible to balance the additional transport capacity on the fore deck against the costs of delays Fraction Delayed Trips [>6hrs, %] Effect of Tolerable Maximum Rigid Body Acceleration on Profit and Reliability calm water profit VSR Criterion for Tolerable Rigid Body Acc at the Bow [SDA, m/s] > 6hrs Delay % Profit Figure 3: Effect of VSR criterion on economy 9 CONCLUDING REMARKS A simple method to account for the contribution of the vertical plane whipping response to the vertical accelerations of a ship was derived from of tests with a flexible model Although the method needs futher validation and a better theoretical foundation, the results suggest that in the present case (a fast slender container ship with relatively low stiffness): The statistical nature of the whipping response yields a significant contribution in the extreme values A negative exponential distribution fits the whipping contribution quite well Profi in % Turnover A simple addition of this result and the traditional assumption for the rigid body motions (a Rayleigh distribution) yields a good representation of the sum of both contributions The effects of wave condition, speed and heading on the mean whipping amplitude can be estimated well with a single parameter (the product of forward speed and the square of the rms of the relative wave elevation at the bow) Using the above method in scenario simulations showed that: Depending on the prudence of the master, slamminginduced whipping increases the acceleration level by 5-5% A voluntary speed reduction is quite effective in reducing the vertical acceleration components FUTURE WORK Apart from the development of methods to predict the impulsive excitation on first principles, an important task is to obtain criteria for tolerable acceleration levels Reverse engineering from existing trips may offer a way to create an awareness how masters perceive their operational dilemma s An important problem in generalising empirical information is lack of information on the effect of the natural frequency of the hull girder A systematic variation would be interesting in this respect The present work focusses primarily on bow flare slamming A more complete assessment (accounting for instance also for the effects of shipping green water, parametric roll, propeller load variations, etc) is required to put the present results in perspective ACKNOWLEDGEMENTS The inquisitive attitude of the DYLOPROPS consortium in the exploration of propeller loads and their permission to publish the present part of the results as well as the support of my colleagues and the MARIN staff is gratefully acknowledged REFERENCES ALBERTS, PJ, NIEUWENHUIJS, M, Full Scale Wave and Whipping Induced Hull Girder Loads; HYDROELASTICITY IN MARINE TECHNOLOGY, Wuxi, China, 6 BIDLOT, JR, JANSEN, P and ABDALLA, S, Extreme Waves in the ECMWF Operational Wave Forecasting System, 9TH INT WORKSHOP ON WAVE HINDCASTING AND FORECASTING, VICTORIA, BC, CANADA September 4-9, 6

9 3 DALLINGA, RP and DAALEN, EFG VAN, Design for Service, 3 IMTA Conference, Rotterdam 4 DALLINGA, RP, DAALEN EFG VAN, GRIN, R and WILLEMSTEIN, AP, Scenario Simulations in Design for Service, PRADS 4 5 EVANS, J and MARLOWE, P, Quantitative Methods in Maritime Economics, ISBN , Fairplay Publications 99 6 GU, X-K, STORHAUG, G, VIDIC-PERUNOVIC, J, HOLTSMARK, G and HELMERS, JB, Theoretical Predictions of Springing and their Comparison with full scale Measurements, Journal of Ship Mechanics, VOL 7; PART 6, pages -5, 3 7 OCHI, MK and MOTTER, LE, Prediction of Slamming Characteristics and Hull Responses for Ship Design, SNAME, OCHI, MK and BOLTON, WE, Statistics for Prediction of Ship Performance in a Seaway, Int Shipb Progress Vol, AUTHOR S BIOGRAPHY Ir Reint Dallinga holds the current position of Department Manager Seakeeping at Maritime Research Institute Netherlands (MARIN), Wageningen, The Netherlands In this position he is responsible for the development of concepts, expertise and tools that enable the seakeeping group to bridge the gap between hydrodynamic theory and practical ship design and operation