Ship Underkeel Clearance in Waves

Transcription

1 Gourlay, T.P. 007 Sip underkeel clearance in, Proc. Coasts and Ports, Melbourne, July 007 Sip Underkeel Clearance in Waves Tim Gourlay 1 1 Centre for Marine Science and Tecnology, Curtin University of Tecnology, We Australia Abstract A metod is described for combining squat, eel and wave-induced motion calculations into an overall underkeel clearance (UKC) assessment, based on te dynamic draft at all te corners of te sip. Particular attention is given to predicting sip motions in sallow water. Te effects of resonant roll, wave spreading and extreme motions are discussed. A general UKC assessment is proposed, valid for calm water or swell conditions. Te principles are applicable to long-term UKC assessment for dredging optimization, as well as assessing specific s troug port approac cannels, based on real-time or forecast wave conditions. 1 Introduction Te exposed coastlines around Australia and New Zealand mean tat many of our port approaces experience long-period swell conditions. Sip vertical motions due to long-period swells ave contributed to some recent grounding incidents, including Capella Voyager and Ea Honour at Wangarei in 003 (see Having a better understanding of underkeel clearance in is an important issue in our region. By contrast, most ports in Europe and Asia are fairly well-protected from long-period swells. Terefore te study of underkeel clearance in as not received muc attention on a global scale to date. Te application of underkeel clearance calculations in falls into two main categories: 1. Coosing optimum dredging depts for approac cannels, using measured annual wave climate. Developing underkeel clearance guidelines or software, for assessing te safety of specific sip s Here we sall describe ow wave response calculations can be combined wit oter components of underkeel clearance. Metods for accurately calculating wave response in sallow water will also be discussed. Components of underkeel clearance Figure 1 sows te additive components in calculating underkeel clearance (UKC) of a sip in sallow water. Tide Cart datum dept Static UKC Static draft Squat, eel, Nett UKC Figure 1: Components for calculating UKC of a sip in sallow water In order for te to be considered safe, te Nett UKC must always remain greater tan a predetermined safety margin. Te Nett UKC is calculated as follows: [Nett UKC] = [Cart datum dept] + [Tide] [Static draft] [Squat, eel and wave response] (1) According to experiments made by Guliev (1971) and Huuska (1976), te squat of a sip in is very similar to te squat of a sip in calm water. Terefore squat and wave response can be calculated independently and ten te effects added togeter. Heel is also assumed to be uncoupled from squat and wave response. Altoug squat, eel and wave response are calculated independently, tese must be combined togeter before determining te overall. Tis is because tey eac cause vertical motions at different parts of te sip, so tat te combined is less tan te sum of te individual s. Te contribution of squat and eel to UKC will now be described briefly..1 Squat Several metods for predicting sip squat are described in te PIANC (1997) guidelines. For open water or a wide cannel of near-constant dept, a metod tat is suitable for bulk carriers, tankers and containersips is based on Tuck s (1966) sallow-water slender body teory. Tis predicts te and sinkage as s s were = c = c L PP L PP F 1 F F 1 F () s = sinkage at te forward perpendicular due to squat

2 s = sinkage at te aft perpendicular due to squat L PP = sip lengt between perpendiculars U F = = dept-based Froude number g U = sip speed troug water (varies troug ) g = acceleration due to gravity = water dept (varies troug ) = sip s displaced volume c = sinkage coefficient 3 Hull extremities and dynamic draft Te vertical movements of squat, eel and wave response eac affect different parts of te sip s ull, so different parts of te sip s ull sould be considered separately wen calculating underkeel clearance. A useful way of doing tis is to use te concept of dynamic draft, wic is te static draft of eac part of te ull, plus te downward sinkage tat it experiences due to te combined effects of squat, eel and wave response. For example, in calm water a bulk carrier wit level static trim will normally ave significant dynamic trim by te, but very little eel, so te maximum dynamic draft will occur at te (Figure ). Wit swell present and terefore roll, te maximum dynamic draft will often occur at te forward soulders of te bilge corners. c = sinkage coefficient Te equations ave very simple dependence on sip dimensions, wit block coefficient, lengt / beam ratio, beam / draft ratio all captured troug te 3 volumetric coefficient /. L PP According to slender-sip teory, te sinkage coefficients c,c depend only weakly on ull sape, and can be calculated analytically. An improvement to tis metod is to use te above equations, but tune te coefficients to agree wit experimental data. Tis approac as been used by Huuska (1976), Icorels (1980) and Gourlay (006) using model experiments. Ideally, full-scale squat measurements sould be used, suc as te measurements described by Hatc (1999), Härting & Reinking (00) on bulk carriers, or Gourlay & Klaka (to be publised) on containersips.. Heel Heel causes te bilge corner to come closer to te seabed, so must be allowed for wen calculating Nett UKC. During te, bot turning and wind cause te sip to eel. Heel effects are small for bulk carriers, but significant for containersips. For a given eeling moment M, te resulting angle of eel φ (radians), assuming ydrostatic equilibrium, is given by M φ = (3) mggm were m is te sip s mass andgm is te transverse metacentric eigt. Te eel angle φ causes an extra sinkage at te bilge corner, approximately equal to φ times alf te sip s beam. Standard metods exist for calculating te eeling moment M due to turning or wind (see e.g. Clark (005) and IMO (005) respectively). Nett UKC Dynamic draft Figure : Example dynamic draft for bulk carrier wit squat A containersip wit level static trim may ave significant eel due to wind and turning in calm water, so te maximum dynamic draft may occur at te bilge corner (Figure 3). Figure 3: Example dynamic draft for midsip section of eeling containersip A containersip wit static trim by te will often ave its maximum dynamic draft at te, despite te bilge corners aving larger sinkage. Te ull extremities used for calculating static draft, sinkage and dynamic draft are te most vulnerable outward extremities of te ull bottom, as sown in Figure 4. Four points are used for containersips and six points for bulk carriers. Aft post Aft post Port aft soulder Stbd aft soulder Port bilge corner Stbd bilge corner Dynamic draft Nett UKC Port fwd soulder Stbd fwd soulder Forward post Forward post Figure 4: Keel waterplane of containersip (top) and bulk carrier (bottom), sowing ull extremities used for analysis

3 Te overall dynamic draft is te maximum dynamic draft over all te vulnerable extremities of te sip. Tis is te point on te sip most likely to it te bottom. Te Nett UKC is calculated as te available water dept for eac part of te, minus te overall dynamic draft. 4 Sip motion calculations in sallow water In order to calculate te nett underkeel clearance of a sip in sallow water wit present, te eave, pitc and roll of te sip are first calculated in given wave conditions. Bot te amplitude and pase of tese vertical motions must be calculated, in order to correctly combine te motion components into overall vertical motions of eac part of te sip. It is important tat sip motion calculations are performed in sallow water, rater tan deep water. Tis is for several reasons: 1. For a given wave period, te wave lengt is sorter in sallow water tan in deep water. Tis canges te wave exciting forces over te lengt of te sip.. For a given wave period, te wave speed is less in sallow water tan in deep water. Tis canges te wave encounter frequency and sifts te peak reponse to different wave periods. 3. Heave and pitc added mass and damping are generally muc larger in sallow water tan in deep water. Tis tends to reduce te motions. Tese effects combine to give sip motions tat are usually, but not always, smaller in sallow water tan in deep water. Te study of sip motions in deep water is welldeveloped, but in sallow water comparatively little researc as been done. Kim (1968) developed a sip motions teory for arbitrary sip speed in ead seas, but it was only valid for dept / draft ratios greater tan 1.5. Beck & Tuck (197) developed a slender-body teory for sip motions, for zero sip speed, tat was valid for small dept / draft ratios. An alternative strip teory approac for calculating te ydrodynamic coefficients at zero sip speed was developed by Keil (1974). As discussed in Beck (001), tese linear metods ave teir limitations, since sallow-water are inerently nonlinear, and tis nonlinearity sould really be included in te wave excitation forces. At present owever, linear metods are all tat are available for routine use. Sip motion in is te most complicated UKC effect to model. Tis is partly due to te complexity of te analysis, and partly due to te large number of variables. Te list of relevant variables includes: Sip dimensions and weigt distribution Sip eading and speed Water dept Measured significant wave eigt, mean wave period, wave direction, spectral sape Wave attenuation away from wave measurement site However, by performing sensitivity studies on te effect of eac variable, te list of important variables can be decreased sligtly. 5 Initial seakeeping calculations For more efficient UKC assessment, te basic seakeeping properties of example sips can be precalculated, so tat less calculations are involved wen inputting actual measured wave conditions. Te initial calculations can be performed as follows: 5.1 Outputting te correct vertical motions Heave causes te same vertical motions over te wole sip, wereas pitc causes te largest motions at te and, and roll causes te largest motions at te beam ends. In addition, tese motions are all out of pase wit eac oter, so tat te vertical displacements will be very different for eac part of te sip. Typically, vertical displacements will be calculated at te ull extremities as sown in Figure 4. Tese vertical displacements can be calculated geometrically from te output eave, pitc and roll, wit careful treatment of te pase differences between eac motion component. 5. Example sips If te UKC assessment is for only a few specific sip types, tese exact sip dimensions can be used for te seakeeping calculations. If te UKC assessment is to be valid for a wide range of sips, a list of example sips can be cosen for te seakeeping calculations. Te cosen list of example sips will depend on ow muc variation tere is in te total list of sips tat we wis to model. For eac type of sip, e.g. bulk carriers wit reasonably similar lengt-tobeam and beam-to-draft ratios, sip lengt is te most important variable. In tat case, it is possible to interpolate between te pre-calculated results for example sips of different sizes, based on te actual sip lengt. If interpolating between example sips of te same type but different size, care must be taken to account for te roll effects of varying beam, GM and radius of gyration. Metods for coping wit tis will be described in Section 6.

4 5.3 Modelling te full range of wave conditions For eac example sip, motions can be calculated using sallow-water seakeeping software. An example of suc software is Seaway, developed at Delft University (see Tis metod is based on classical wave loads in sallow water, using te correct sip speed and sallowwater wave speed and lengt, and uses Keil s (1974) metod for determining te sallow-water ydrodynamic coefficients. Te initial seakeeping calculations can be designed to cover te full range of encountered wave conditions, as follows: A typical wave spectral sape is cosen tat best represents measured wave spectra in te particular area Due to te near-linearity of te seakeeping metod, all initial calculations are performed using a significant wave eigt of 1.0m A full range of mean wave periods is cosen, e.g. 0 seconds in second increments A full range of wave directions relative to te sip eading is cosen, e.g in.5 increments Tese initial calculations ten yield a matrix of vertical motions over te full range of wave directions and mean wave periods. Wen it comes to predicting sip motions in measured wave conditions, tis matrix can be interpolated to te correct wave direction and mean wave period, and multiplied by te correct significant wave eigt. Example motions for a 30m L PP bulk carrier in ead seas wit significant wave eigt 1.0m are sown in Figure 5, as calculated using Seaway software. Te significant vertical displacements sown correspond to te average amplitude of te ⅓ largest motions in an irregular seaway of a given mean wave period. Significant vertical displacement (metres) Bow Stern Forward soulders Aft soulders In ead seas, as sown ere, te port and starboard sides experience te same motions, owever for general wave directions tey will be different. Also, for wave directions closer to te beam, te forward and aft soulders experience larger motions tan te and. For tis bulk carrier in ead seas, te combined effect of wave response and squat by te mean tat, for level static trim, te is most in danger of grounding. For wave directions closer to te beam, te combined effect of squat and means tat te port or starboard forward soulder will normally be most at risk of grounding. 6 Adjusting te seakeeping outputs Te results from te initial seakeeping calculations sould now be adjusted to allow for uncertainty in te peak roll response, and wave spreading. 6.1 Uncertainty in peak roll response For wave directions close to te beam, roll can become te most important factor governing UKC. Roll as te specific problem tat it is fairly narrow-banded about te sip s natural roll period. Terefore tere is a risk of seriously underpredicting te roll motion if te seakeeping predictions are not exactly rigt. Te major factors affecting natural roll period are sip beam, transverse GM, and roll inertia. Due to te difficulty in accurately specifying transverse GM and roll inertia, it is a good idea to artificially widen out te roll peak, so it covers a wider range of natural roll periods. Tis is done only at ull extremities on te bilge corners, for eadings close to te beam. Wen modelling specific sips, only a small amount of widening is needed, owever wen interpolating example sips to different sip dimensions, more widening is needed to make sure tat te roll peak is not missed. 6. Wave spreading Te seakeeping calculations usually performed are for uni-directional or long-crested. In reality, are normally sort-crested, wit variations in wave direction about an average value. Te tends to decrease te peak motions, as compared to a long-crested seaway. In order to more accurately simulate a sort-crested seaway, a spreading function may be applied (see e.g. Lloyd 1989). Te results for eac wave direction are modified by taking te weigted average of te surrounding wave directions, to account for wave spreading Mean wave period (seconds) Figure 5: Significant vertical displacements for a 30m L PP bulk carrier in ead seas of varying mean wave period. Significant wave eigt = 1.0m, spectrum = JONSWAP.

5 7 Motions for actual wave conditions Having pre-calculated eac sip s vertical motions over a full range of wave directions, periods and eigts, results can now be calculated for te actual wave conditions being considered. Tese wave conditions may be: Historical wave conditions, a full set of wic is used for long-term UKC calculations, suc as determining optimal dredging depts for a port approac cannel Forecast wave conditions, for planning s witin te wave forecast period Real-time wave conditions, for monitoring UKC for an imminent, or during a Firstly, mean wave period, significant wave eigt and wave direction must be calculated for te entire, using wave attenuation from te measurement or forecast location. Te required complexity of te wave modelling depends on te geograpy. Te sip s course along eac part of te, togeter wit te wave direction along eac part of te, gives te wave eading relative to te sip along eac part of te. Significant vertical amplitudes for eac ull extremity can now be interpolated to te correct wave eading, wave period and wave eigt for eac part of te. 8 Maximum likely motions Wave-induced motions, like a real seaway, are a statistical penomenon. It is always possible to encounter a larger set of, and ence ave larger motions, tan any reasonable estimate made in advance. Hence coosing a wave-induced motions is a matter of coosing an acceptably low grounding risk and working wit tis. An irregular sea as a wide variety of different wave eigts and ence wave-induced vertical motions. We wis to find not just te vertical motion on a single wave, but te maximum likely motion over a wole, or even better over a large number of s. Te significant amplitudes described above ( z 1/3 ) represent te average of te igest 1/3 vertical amplitudes, so te largest motions are considerably more tan tis. For linear seakeeping metods, suc as te Seaway software and most oter seakeeping software, a Rayleig distribution can be used to estimate maximum values wit a given probability of exceedence. Suppose we coose a vertical motion z. Ten te Rayleig distribution (see e.g. Battacaryya 197) tells us tat z Pr( z > z = ) exp z1/3 (4) By calculating te average number of longer-period experienced over te dangerous part of te ( N ) and coosing an acceptable exceedence probability for eac ( P ), te probability tat te will be exceeded on eac wave is P Pr( z > z) = N (5) z = exp z1/3 Terefore te vertical motions is given by z z 1/3 = N 0.5 ln P (6) Te number of experienced over te dangerous part of te ( N ) can be estimated based on te mean wave period, and te time tat te sip spends in te sallow, exposed part of te. Te acceptable grounding probability for eac ( P ) can be calculated based on longterm grounding probabilities, as mentioned in te PIANC (1997) guidelines. For example, Savenije (1996) describes te acceptable grounding probabilities used for assessing safety in te Euro-Maas cannel. In tat case it is assumed tat 1 in 10 bottom touces will result in more tan minor damage, and te acceptable probability for aving more tan minor damage is 10% over 5 years. Tis allows te acceptable bottom toucing probability ( P ) to be determined, based on te expected number of s over a 5 year period. Te cosen 5-year grounding probability sould also depend partly on te type of seabed and terefore te consequences of grounding. Using typical values of N and P, equation (6) gives a wave-induced motion z in te order of times te significant amplitude. Te resulting waveinduced motion is different for eac ull extremity, set of wave conditions, and position in te.

6 9 Overall squat, eel and wave motions Metods ave been described for calculating te squat, eel and wave-induced motion s independently. Tese can now be added togeter, to give te total squat, eel and wave-induced motion, wic must be done using te correct values for eac ull extremity. As described in Section 3, te sinkage at eac ull extremity due to squat, eel and, can be added to te static draft at eac ull extremity, to give te dynamic draft at eac ull extremity. Te maximum dynamic draft over all te ull extremities is ten te overall dynamic draft. Te difference between te overall dynamic draft and te available water dept is te nett underkeel clearance. In calm water, we can assess overall safety based on te PIANC (1997) guidelines. Tese suggest tat te Nett UKC sould never fall below a certain safety margin, wic is suggested to be 0.3m for a muddy seabed, 0.5m for a sandy seabed, and 1.0m for a rocky seabed. Terefore tis metod is deterministic, in tat fixed formulae are used for te squat and eel s, and te safety margin ensures sufficient clearance for te cases were tese formulae under-predict te squat or eel. Wit swell present, te metod canges from a deterministic to a probabilistic assessment. In tat case, te PIANC (1997) guidelines suggest tat te safety sould not be needed, since grounding probabilities ave been calculated explicitly, and are required to be kept below a certain value. However, te ideal UKC assessment needs to be valid for bot calm water and swell conditions, wit a smoot ion between te two. For example, an obvious requirement is tat te static UKC in any sort of swell conditions must never be smaller tan te calm-water value. One simple approac is to include te safety margin in all conditions, so tat te metod will be valid wen no are present. In swell conditions, tis safety serves as an uncertainty in te wave response calculations. A fixed serves better tan a percentage uncertainty, since wave-induced motions are predicted to be very small under some conditions. Terefore in calm water te approac follows te PIANC guidelines in te usual manner, wile in swell conditions te probabilistic assessment remains valid, wit te safety serving as an uncertainty in te wave response calculations. Corrections to tis metod can ten be made based on quantified errors in te seakeeping analysis. 10 References Beck, R.F. (001) Modern computational metods for sips in a seaway. Trans. SNAME 109. Beck, R.F. & Tuck, E.O. (197) Computation of sallow water sip motions. Proc. 9 t Symposium on Naval Hydrodynamics, Paris. Battacaryya, R. (197) Dynamics of Marine Veicles. Wiley Series on Ocean Engineering. Clark, I.C. (005) Sip Dynamics for Mariners. Te Nautical Institute, London. Gourlay, T.P. (006) Flow beneat a sip at small underkeel clearance. J. Sip Researc 50(3). Gourlay, T.P. & Klaka, K. Full-scale measurements of containersip sinkage, trim and roll (under review). Guliev, J.M. (1971) On squat calculations for vessels going in sallow waters and troug cannels. PIANC Bulletin, No. 1. Härting, A. & Reinking, J. (00) SHIPS: A new metod for efficient full-scale sip squat determination. Proc. PIANC 00, Sydney. Hatc, T. (1999) Experience measuring full scale squat of full form vessels at Australian ports. Proc. Coasts and Ports 1999, Pert. Huuska, O. (1976) On te evaluation of underkeel clearances in Finnis waterways. Helsinki University of Tecnology, Sip Hydrodynamics Laboratory, Otaniemi, Report no. 9. ICORELS (International Commission for te Reception of Large Sips) (1980) Report of Working Group IV. Supplement to PIANC Bulletin No. 35. International Maritime Organization (005) Revision of te Intact Stability Code. Submitted by Japan, IMO sub-committee on stability and load lines and on fising vessels safety, 48t Session, June 005. Keil, H. (1974) Die Hydrodynamisce Kräfte bei der periodiscen Bewegung zweidimensionaler Körper an der Oberfläce flacer Gewasser. Berict 305, Institut für Sciffbau der Universität Hamburg. Kim, C.H. (1968) Te influence of water dept on te eaving and pitcing motions of a sip moving in longitudinal regular ead. Sciffstecnik, Vol. 15, No. 79. Lloyd, A.R.J.M. (1989) Seakeeping sip beaviour in roug weater. Ellis Horwood. PIANC (1997) Approac cannels: A guide for design. Supplement to PIANC Bulletin, No. 95. Savenije, P. (1996) Probabilistic admittance policy deep draugt vessels. PIANC Bulletin, No. 91. Tuck, E.O. (1966) Sallow water flows past slender bodies. Journal of Fluid Mecanics, Vol. 6.