Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules

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Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules S.S. Bennett n, D.A. Hudson, P. Temarel Fluid–Structure Interactions Research Group, Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK

a r t i c l e i n f o

abstract

Article history: Received 25 June 2013 Accepted 25 May 2014

It is important to assess the consequences of ship encounters with abnormal waves due to the perceived dangers of such encounters. A starting point for this is the assessment of global loads, with a focus on examining how the design rules fare with respect to loads induced by abnormal wave encounters. This paper presents the results of an experimental investigation into the global wave induced loads experienced in a range of abnormal sea states. Results are obtained for a segmented, flexible backbone model of a typical naval frigate. Abnormal wave encounters result in a significant increase in the global waveinduced loads compared to the equivalent random sea, with slamming becoming considerably more severe. Through comparisons with the experimental measurements it is concluded that the design rules which allow for an extreme wave encounter provide a reasonable safety margin for the global loads in abnormal waves, although discrepancies occur towards the aft of the vessel. Further investigation of the amount and conditions in which the design rules may be exceeded by an abnormal wave encounter is required. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Abnormal waves Rogue waves Wave–vessel interactions Experiments Global loads Ship design rules

1. Introduction Abnormal, freak or rogue waves are a dangerous phenomenon which causes severe structural damage and operation disruption to the encountering vessel and, in some cases, loss of the vessel and crew. The passenger ship Voyager experienced severe roll motion, control room flooding and a loss of electrical systems in 2005 (Bertotti and Cavaleri, 2008). FPSO Schiehallion suffered deformation damage to plating 15–20 m above the waterline from severe bow slamming (Stansberg, 2000). Both of these examples are documented encounters with abnormal waves. Unexplained losses of the M/V Munchen in 1978 (Liang, 2007) and the M/V Norse Varient and M/V Anita simultaneously in 1973 (Kjeldsen, 2000) are attributed to abnormal wave encounters. The aforementioned examples illustrate the importance of assessing the risks associated with encountering abnormal waves from a structural viewpoint and investigating the consequences for the ship structural design; hence, by implication, ship design rules. Global loads, especially when slamming is involved, should be assessed using a hydroelastic analysis, which accounts for the inherent coupling between the hydrodynamic actions on a ship and the distortions of the ship due to the waves present. Such an analysis is conducted experimentally in this paper using a flexible model hull.

n

Corresponding author. Tel.: þ44 2380 593035. E-mail address: [email protected] (S.S. Bennett).

http://dx.doi.org/10.1016/j.jfluidstructs.2014.05.009 0889-9746/& 2014 Elsevier Ltd. All rights reserved.

Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Flexible models can be wholly elastic or constructed of rigid hull segments connected by either a flexible backbone or flexible hinges (Denchfield, 2011) and have been used for investigations of ships in severe wave conditions. Drummen et al. (2009) use a hinged model of a containership to measure vertical bending moments in steep regular and random waves. Wu et al. (2003) use a wholly elastic model of an S175 containership in steep random waves to assess vertical bending moments. The results are used to provide further detail on the nature of the vertical bending moments, as well as verify predictions from hydroelasticity theories. Dessi and Mariani (2008) and Lavroff et al. (2010) analyse slamming induced loads of high speed monohull and catamaran hulls. A backbone model with a non-uniform cross-section backbone is used by Dessi and Mariani (2008) whereas Lavroff et al. (2010) use a hinged model. Miyaki et al. (2009) perform an experimental study of the response of a mega containership in regular and irregular waves. Analysis looks at the influence of springing and whipping events on the magnitude of the vertical bending moment in a range of wave heights and frequencies. The experimental investigations of a ship in abnormal waves to date tend to have used a rigid model. The majority of investigations have taken place at zero speed, for example Guedes-Soares et al. (2006) measure the vertical bending moment and two degree of freedom motions (heave and pitch) of an FPSO in abnormal seas constructed of three segments joined by instrumented steel plates to measure bending. In a similar manner, Clauss (2008) investigates a semi-submersible in abnormal waves to look at heave and splitting forces. Only limited investigations have been carried out that involve a vessel in abnormal waves at forward speed. Clauss (2009) investigates one speed and measures vertical bending moment at only one location along the vessel whilst Kinoshita et al. (2006) investigate a fully flexible model of a containership in transient waves at two speeds. This paper presents experimental results for the vertical bending moments at various positions along a naval frigate, travelling at its service speed in a range of head regular and long-crested irregular (random and abnormal) waves, obtained using a segmented, flexible backbone model. Probability of exceedence calculations are carried out for the ship responses and an analysis of the whipping response is presented. The results are compared to naval ship design rules from classification societies, namely Lloyd's Register (LR), Det Norske Veritas (DNV) and Bureau Veritas (BV). The suitability of current ship design rules for producing ship designs capable of withstanding abnormal waves is discussed. 2. Experimental set-up 2.1. Test facility Tests were conducted in a towing tank 60 m long, 3.7 m wide and 1.86 m deep with a maximum carriage speed of 4.5 ms  1. Unidirectional (long-crested) waves were generated using a single, motor-driven paddle wavemaker. Wave reflections from the absorption beach measured using the technique of Isaacson (1991) were less than 10%. 2.2. Flexible model hull A typical naval frigate hull with the principal particulars in Table 1 was tested. The hull was a segmented, flexible backbone model constructed of four rigid segments attached to a uniform, aluminium backbone beam. The aluminium backbone beam was carefully selected to ensure that the natural frequency and the bending stiffness of the model hull correctly represented those of the full scale vessel, represented as a uniform backbone beam. Based on literature four segments is sufficient to obtain the lower vertical bending modes whilst a uniform cross-section backbone allows the correct scaling of the 1st vertical bending mode (Denchfield, 2011). It is considered that the flexible backbone technique is sufficient to approximate the bending stiffness of the full scale ship appropriately; hence flexible backbone models have been used in previous research (e.g. Takaoka et al., 2012) allowing the modelling of vertical bending moment, whipping and slamming response. Fig. 1(a) is a schematic of the hull arrangement whilst Fig. 1(b) is the body plan. The uniform backbone of the model, with a thin-walled rectangular cross section, was designed to match the predicted natural frequency of the 2-node vertical bending mode (obtained from non-uniform Timoshenko beam theory). Table 2 gives the predicted and measured (from an impact hammer test) dry 2-node natural frequencies at full scale. Fig. 2 presents Table 1 Principal particulars of typical naval frigate at model and full scale. Parameter

Model

Ship

Length overall, LOA (m) Length between perpendiculars, LBP (m) Breadth, B (m) Draft at amidships, T (m) Displacement, Δ (kg, Tonnes) LCG aft amidships (m) Pitch gyradius, kyy (%LOA) Ship service speed, Vs (ms  1, knots) Scale

2.60 2.52 0.29 0.096 29.40 0.091 23.21 1.40 43.62

113.40 109.72 12.36 4.19 2921 3.96 24.0 18.0 1

Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 1. (a) Flexible model schematic diagram and (b) naval frigate body plan.

Table 2 Experimental and predicted 2-node natural frequencies (full scale). Model

ω2 (rad/s)

Experiment Non-uniform Timoshenko

14.28 14.69

Fig. 2. Measured and predicted (Timoshenko non-uniform) mode shapes for 2-node bending.

the predicted and measured dry hull 2-node mode shapes, where the measured mode shape was obtained from analysis of the beam vibratory response measured during the impact hammer test using an accelerometer located at various points along the beam length. Measurements were taken during experiments of rigid body motions and vertical bending moments. Table 3 gives details of the instrumentation system including sample rate and location of each sensor from the stern (x¼0).

2.3. Abnormal wave definition Abnormal waves were defined primarily with respect to the encountering ship, using the Severity Index, IS. This is an extension of the Length Index (Denchfield et al., 2010) which assumed that for a wave to be abnormal IL ¼

LOA r10:0; HR

ð1Þ

where LOA is the overall ship length and HR the trough-to-crest abnormal wave height. The Severity Index includes an allowance for Froude number because abnormal wave encounters become more severe as Froude number increases due to the corresponding increase in wave steepness (Denchfield et al., 2010). The results from the experiments conducted in Denchfield et al. (2010) gave a relationship between Froude number and the steepness of the encountered wave, leading to a Severity Index of IS ¼

i LOA h  0:3485ðF 0N Þ2 þ 0:0462 F 0N þ 0:9959 ; HR

ð2Þ

where F 0N is the Froude number normalised with respect the Froude number at the ship service speed. At zero speed the Severity Index reduces to the original Length Index given in Eq. (1). Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Table 3 Details of the instrumentation system. Measurement

Wave elevation Heave Pitch

Instrumentation

Sample rate (Hz)

Resistance based wave probe Potentiometer Potentiometer 3  full bridge strain gauge arrangements

Vertical bending moment

Location (longitudinal) Level with amidships (transverse) 0.9 m from tank centreline 0.46%LOA (LCG) from stern 0.46%LOA (LCG) from stern 0.25%LOA from stern 0.50%LOA from stern 0.75%LOA from stern

100 100 100 100

Table 4 Statistical properties of irregular sea states (full scale). Sea state

Location

HS (m)

TP (s)

1 2 3

South Atlantic North Atlantic Southern Ocean

4.32 4.71 6.10

10.57 10.30 11.56

2.4. Test program Tests were conducted in head regular and irregular (random and abnormal) long-crested head waves at the ship service speed (18 knots full scale). Regular waves were tested at three heights corresponding to H/LOA values of 0.02, 0.04 and 0.05. Long-crested irregular waves were tested for three sea states contained in the sea data in Lloyd's Register Rules for the Classification of Naval Ships (Lloyd's Register, 2012) and are representative of South Atlantic, North Atlantic and Southern Ocean conditions. Table 4 gives the statistical properties for each sea state, where HS is the significant wave height and Tp the peak wave period of the sea state, which were tested as random and abnormal seas. Abnormal waves were generated within a random background using the optimisation method applied in the previous research (Bennett et al., 2012a, 2013). Work in Bennett et al. (2012a) compared this optimisation technique to alternative rogue wave generation techniques, including the NewWave technique (which generates the most statistically likely extreme wave to occur in a seastate). This work found the optimisation technique to be the most suitable technique for the intended purpose of investigating ship responses in rogue waves (Bennett et al., 2012a) and as such was implemented in this research. A short overview of the technique is given here for clarity. An initially random sea constructed of J ¼100 regular wave components with random phases can be calculated using η ¼ ∑100 j ¼ 1 Aj cos ðωj t þ kj x þ ϕj Þ where ϕj is the jth random phase. By defining a target (abnormal) wave in terms of its troughto-crest height (HR), the J random phases can be modified at each iteration loop until the target wave is formed in the random sea. Replacing ϕj with the new (optimised) phases calculates the optimised abnormal sea profile. This technique has been proven to generate abnormal waves within a random sea state that can still be considered to have maintained the stochastic nature of a random sea, as each time the optimisation is carried out (for particular sea state properties) a different optimised sea state will be achieved (Clauss, 2008). The abnormal (target) trough-to-crest wave height input value was chosen as 11.34 m (at full scale), which gave a Severity Index of 10.0 at zero speed and 6.94 at 18 knots and allowed a direct comparison to be made as to the effect of an abnormal wave occurring in different random seas. Experimentally generated wave profiles (see Fig. 8 in Section 3) had a wave height which was within 9% of this input value which, based on previous studies (Bennett et al., 2012a), was considered acceptable. Table 5 summarises the purpose of each set of experiments. Each individual test was repeated 3 times and the results presented are the average of these three tests. Test runs were of 80 s duration. This test duration was selected as sufficient based on the International Towing Tank Conference (ITTC) Recommended Procedures and Guidelines for measuring loads and responses during seakeeping experiments in a rarely occurring event (ITTC, 2008).

3. Experimental results 3.1. Regular wave results Whilst the focus of this paper is responses in abnormal waves, regular wave responses were initially studied in order to investigate levels of experimental uncertainties (Section 5), and look at the behaviour of the ship (such as the onset of slamming). Figs. 3 and 4 present the heave and pitch RAOs at 18 knots. The experimental values of H/LOA translate to regular wave heights of 2.27, 4.54 and 5.67 m at full scale. Each data point represents the average of three repeat tests. Some variation in the magnitude of the RAOs, both heave and pitch, is observed as the wave height (hence H/LOA) increases. This is particularly around the peak of the RAO where the largest responses were observed, indicating some Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Table 5 Summary of experiments. Experiment

Purpose

Regular waves VS ¼1.4 m/s (18 knots full scale) H/LOA ¼ 0.02, 0.04 and 0.05

 Assess experimental uncertainties  Assess influence of increasing wave height on ship behaviour  Assess the onset of slamming

Random seas VS ¼1.4 m/s (18 knots full scale)

 As a comparator for the results for ship behaviour in abnormal waves

Abnormal seas VS ¼1.4 m/s (18 knots full scale) IS ¼ 6.94 at 1.4 m/s

    

Assess the influence of abnormal waves on ship behaviour Investigate the influence of slamming in abnormal wave Investigate the likelihood of whipping and springing Assess the probability of exceedence of ship responses Assess the suitability of current design rules

Fig. 3. Measured heave RAOs at 18 knots and H/LOA ¼ 0.02, 0.04 and 0.05 where ζ is the measured heave amplitude and η the wave amplitude.

Fig. 4. Measured pitch RAOs at 18 knots and H/LOA ¼ 0.02, 0.04 and 0.05 where θ is the measured pitch amplitude and k the wave number.

moderate nonlinear effects in the motions of the vessel as the wave height increases. This result is in-line with that seen in Drummen et al. (2009) in terms of the degree of nonlinearity present when relative motions were large. In pitch the nonlinearities are seen as a reduction in the RAO value whereas in heave they appear as a slight increase in the RAO value. Figs. 5–7 show the vertical bending moment (VBM) RAOs at the three locations – 0.25LOA (aft quarter), 0.5LOA (amidships) and 0.75LOA (forward quarter) from the stern at 18 knots. At midships the results, as with the heave and pitch RAOs, show only moderate change in the RAO with wave height. At the forward and aft quarters there is a clear increase in the magnitude of the RAOs with increased wave height. In both cases the peak RAO magnitude at H/LOA ¼0.05 is approximately Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 5. Measured VBM RAOs at aft quarter at 18 knots and H/LOA ¼0.02, 0.04 and 0.05.

Fig. 6. Measured VBM RAOs at midships at 18 knots and H/LOA ¼0.02, 0.04 and 0.05.

double that at an H/LOA of 0.02. Significant amounts of slamming were observed during experiments, in particular at the bow of the vessel. Hence the significant nonlinearities in the vertical bending moment response at the forward and aft quarters, which become more dominant as the wave height increases, can be attributed to the observed slamming.

3.2. Irregular wave results Vertical bending moments, as well as heave and pitch motions, were measured in the abnormal wave conditions given in Table 4. The results are presented in Fig. 8, along with the corresponding wave profile, for the abnormal wave part of the wave record (corresponding to the worst case slamming condition for the ship in each case). As previously shown for rigid body motions (Bennett et al., 2013) and demonstrated here for global loads, a significant peak is seen in the vertical bending moment at each location along the ship when the abnormal wave is encountered. Furthermore significant asymmetries can be seen between the hogging (positive) and sagging (negative) vertical bending moments. Of importance in abnormal waves is the maximum vertical bending moment variation with maximum wave height. Figs. 9–11 present these results for the forward quarter, amidships and aft quarter. The maximum vertical bending moments experienced in the abnormal seas are, in general, greater than those in the random seas at the same maximum wave height. The random sea results show a linear increase in maximum bending moment with maximum wave height. Interestingly, Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 7. Measured VBM RAOs at the forward quarter at 18 knots and H/LOA ¼ 0.02, 0.04 and 0.05.

however, as the results move into the abnormal wave height range of the data (i.e. Hmax 48 m) the trend in maximum bending moment increase is more akin to an exponential form. This is particularly evident in the results for amidships (Fig. 10) and the aft quarter (Fig. 11). The switch from a linear to exponential trend indicates the wave height at which nonlinear influences, such as slamming, begin to dominate the total response of the vessel. The influence of an abnormal wave occurring in a sea state is likely to be severe. Table 6 presents the increase in the maximum vertical bending moments recorded at each location in abnormal compared to random seas, as a ratio of the abnormal to random response. In each case the random sea has the same statistical properties as the abnormal sea. The increase in response in the abnormal wave is significant at all locations along the ship, being at least 1.2 times that in the random sea. This can further be seen when looking at the maximum and significant one-third and one-tenth hogging and sagging vertical bending moments in each sea state, and again calculating the ratio of abnormal to random response at each location and in each sea state. The results for this comparison are given in Table 7 for the maximum values, Table 8 for the one-third values and Table 9 for the one-tenth values. These statistics show the hogging one-third vertical bending moment to be generally between 1.22 and 2.31 times greater in abnormal waves whereas the sagging one-third vertical bending moment is generally between 1.08 and 1.91 times greater. For the significant one-tenth values an abnormal wave results in a 1.49–3.29 increase in hogging and 1.20–1.56 increase in sagging. The significant increase show in, not only the maximum vertical bending moment, but also the significant one-third and one-tenth values may have implications when assessing the ability of the design rules to encompass the risks associated with abnormal waves. The experimental data consistently showed that in both the abnormal and random sea cases M MAX 4M 1=10 4 M1=3 . Correspondingly, the data presented in Tables 7–9 also demonstrates that, in the majority of cases ðMABNORMAL;MAX =M RANDOM;MAX Þ 4 ðMABNORMAL;1=10 =M RANDOM;1=10 Þ 4 ðMABNORMAL;1=3 =M RANDOM;1=3 Þ; the few cases where this is not the case is because the increase in M RANDOM is greater than, or comparable to, the increase in M ABNORMAL from the significant one-third to significant onetenth, or significant one-tenth to maximum value. A further point to note is the non-uniformity in the increase in the bending moment ratio across the three different geographic locations assessed. This can be considered to be due to the ship interacting differently with the various irregular seas. A further contributing factor to the non-uniformity may be the varying levels of ship emergence observed in the different sea states (see Section 3.2.1). The values of bending moment ratio presented in Tables 7–9 are provided to present an overall picture of the influence of an abnormal wave encounter – which appears to be, on average, a two-fold increase in the hogging bending moment and a 1.5 times increase in the sagging bending moment compared to those in a random sea, rather than to identify any trends between the different geographic locations. 3.2.1. Slamming response Fig. 12 presents the percentage of slams occurring at different severities of slamming length (or forefoot emergence, defined as a percentage of the ship's length) in random and abnormal waves, for each of the three sea states. Results were obtained using the technique presented in Bennett et al. (2012b). The distribution of slams in random seas appears more even across the range of slamming lengths. 40–60% of slams in abnormal seas occur with a forefoot emergence of 25%LOA, compared to 15–35% in random seas. This demonstrates that the presence of an abnormal wave greatly increases the number of severe slams occurring. The level of bow emergence can also be considered to have an effect on the magnitude of the increase in vertical bending moment from random to abnormal seas (as presented in Tables 7–9), as naturally the increased percentage of severe slams observed in abnormal seas will affect the Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 8. Experimental results for (a–f) South Atlantic, (g–l) North Atlantic and (m–r) Southern Ocean conditions. Results are shown for (a,g,m) wave profile, (b,h,n) heave, (c,i,o) pitch, (d,j,p) VBM at 0.75LOA, (e,k,q) VBM at 0.5LOA and (f,l,r) VBM at 0.25LOA from the stern (full scale).

magnitudes of the vertical bending moment measured. However, as stated in Section 3.2 it will be this, combined with the differing interactions between the ship and the sea state in question, that will lead to the observed non-uniform increases in the bending moment ratio at the different geographic locations.

3.2.2. Whipping response The total vertical bending moment at amidships can be decomposed using filtering techniques into the steady state wave response and the whipping response. Application of a low pass filter gives the wave response whilst application of a high pass filter gives the whipping response. Fig. 13 shows the decomposition of experimental results for vertical bending moment into the wave response and whipping response, for both a random and an abnormal sea in North Atlantic conditions. It should be noted that in Fig. 13(a) there is also a high frequency steady state component visible which indicates the presence of springing. This is less evident in the abnormal sea state in Fig. 13(b). Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 9. Maximum VBM variation with maximum wave height in random and abnormal waves at the forward quarter and 18 knots (full scale).

Fig. 10. Maximum VBM variation with maximum wave height in random and abnormal waves at amidships and 18 knots (full scale).

Fig. 11. Maximum VBM variation with maximum wave height in random and abnormal waves at the aft quarter and 18 knots (full scale).

A whipping amplification factor can be calculated as the ratio of the total dynamic response to the total wave response as (Storhaug et al., 2012; Lee et al., 2012) γ¼

MTOTAL ; M WAVE

ð3Þ

for both hogging (positive) and sagging (negative). Fig. 14 presents hogging and sagging whipping amplification factors for random and abnormal sea states, for the most severe total response peak in each sea state and for each direction. In sagging, the whipping amplification factor in random seas is reasonably constant (approximately 1.5) whilst the same value for abnormal seas increases from 1.5 in the less severe abnormal sea to 2.5 in the most severe abnormal sea. In hogging and the Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Table 6 Increase in VBM in abnormal compared to random seas, presented as a ratio of abnormal-to-random VBM. Sea state

Location

1 2 3

MABNORMAL,

South Atlantic North Atlantic Southern Ocean

MAX/MRANDOM, MAX

0.75LOA

0.50LOA

0.25LOA

1.95 1.45 1.73

1.81 1.44 2.51

1.61 1.22 2.29

Table 7 Increase in VBM in abnormal compared to random seas, presented as a ratio of abnormal-to-random maximum VBM. Sea state

1 2 3

Location

South Atlantic North Atlantic Southern Ocean

Hogging MABNORMAL,

MAX/MRANDOM, MAX

Sagging MABNORMAL,

MAX/MRANDOM, MAX

0.75LOA

0.50LOA

0.25LOA

0.75LOA

0.50LOA

0.25LOA

3.06 2.81 3.13

2.24 4.06 4.69

1.87 2.68 3.87

1.54 1.23 1.15

1.58 1.10 1.49

1.84 1.14 1.65

Table 8 Increase in VBM in abnormal compared to random seas, presented as a ratio of abnormal-to-random significant one-third VBM. Sea state

1 2 3

Location

South Atlantic North Atlantic Southern Ocean

Hogging MABNORMAL, 1/3/MRANDOM, 1/3

Sagging MABNORMAL, 1/3/MRANDOM, 1/3

0.75LOA

0.50LOA

0.25LOA

0.75LOA

0.50LOA

0.25LOA

1.62 2.21 2.25

1.22 1.58 2.16

0.99 2.31 1.89

0.98 1.14 1.57

0.92 1.16 1.55

1.08 1.91 1.50

Table 9 Increase in VBM in abnormal compared to random seas, presented as a ratio of abnormal-to-random significant one-tenth VBM. Sea state

1 2 3

Location

South Atlantic North Atlantic Southern Ocean

Hogging MABNORMAL, 1/10/MRANDOM, 1/10

Sagging MABNORMAL, 1/10/MRANDOM, 1/10

0.75LOA

0.50LOA

0.25LOA

0.75LOA

0.50LOA

0.25LOA

2.73 2.71 2.17

1.69 2.61 3.29

1.49 2.91 2.78

1.28 1.32 1.20

1.26 1.26 1.40

1.37 1.56 1.46

Fig. 12. Percentage of slams in random and abnormal waves with different severities of forefoot emergence (slam length) for (a) South Atlantic conditions, (b) North Atlantic conditions and (c) Southern Ocean conditions.

Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 13. Demonstration of decomposing the total bending moment response at amidships into (steady state) wave response and whipping response for (a) random and (b) abnormal seas for the North Atlantic conditions.

least severe sea states the random sea has a whipping amplification factor of approximately 1.45, increasing in a linear manner to approximately 1.6 in the more severe Southern Ocean conditions. The equivalent abnormal sea value also increases with severity but to a greater extent, going from approximately 1.4 in the least severe South Atlantic conditions to approximately 1.9 in the most severe abnormal sea of the Southern Ocean. These results demonstrate that whipping contributes a significant amount to the total vertical bending moment in both the random and the abnormal seas. Recent research into voyage analysis by Storhaug et al. (2012) derives maximum whipping amplification factors of 1.33 in both hogging and sagging conditions, and considers this to be an extreme case. Lee et al. (2012) state that, using a nonlinear analysis, for a large containership in irregular waves the hogging amplification factor is 1.42 whilst the sagging amplification factor is 1.98, both of which are in excess of the design rules. Therefore, although the level of whipping in the abnormal seas is likely to exceed that allowed by the design rules this may well also be the case for the random seas, hence there may be dangers associated with the whipping response of the ship regardless of whether an abnormal wave is encountered. An abnormal wave is, however, likely to produce larger whipping response than a random sea, as illustrated in Figs. 9–11. 3.2.3. Probability of exceedence The probability of exceedence for the motions and vertical bending moments measured in experiments was calculated as (Cox and Scott, 2001) P ex ¼

i ; N þ1

ð4Þ

where i is the rank of each data point (ascending to descending magnitude) and N is the total number of data points measured (i.e. the total number of peaks in the response trace). Results are compared to the Rayleigh distribution, calculated as "  2 # x P ex ¼ exp  8 ; ð5Þ XS where x is the crest (positive peak) height of the parameter in question (i.e. heave, pitch or vertical bending moment) and XS is the significant height of the parameter. Extreme responses were also compared to the exponential distribution which has the form    x ; ð6Þ P ex ¼ exp λ XS where λ is a constant, taken as 4.0 for the rigid body motions and 3.0 for the vertical bending moments in this research. A smaller value of λ indicates a greater deviation from the Rayleigh distribution. Fig. 15 compares the experimental probability of exceedence values to the predicted distributions for rigid body motions. The experimental results are for heave and pitch, for the three random and abnormal sea states. Fig. 16 shows the same comparison for the vertical bending moments at the forward and aft quarters and amidships. For both figures the horizontal axis is (x/XS) for the relevant response, the subscript S denotes the significant value of the entire record. Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 14. Experimental whipping amplification factor, γ, for random and abnormal seas for (a) sagging and (b) hogging conditions for each sea state tested.

Fig. 15. Probability of exceedence of (a,b) heave and (c,d) pitch in (a,c) random seas and (b,d) abnormal seas from experimental results, compared to the Rayleigh distribution and, in the case of abnormal waves, the exponential distribution.

Heave and pitch results in random seas closely follow the Rayleigh distribution. The results in abnormal waves follow the Rayleigh distribution until x=X S  0:6 in both cases. Above x=X S  0:6 the probability of exceedence is greater than that predicted by the Rayleigh distribution and the exponential distribution provides a better match. It can also be seen from Fig. 15 that whilst the probability of exceedence in pitch is similar at the tail of the distribution, regardless of sea state, there is slightly more variation in the heave results which appear to suggest the North Atlantic as a worst case rather than the Southern Ocean. The probability of exceedence of the vertical bending moments show significantly different trends to those observed in the rigid body motions. The Rayleigh distribution is exceeded at approximately x=X S  0:5 in both the random and abnormal seas, where the value of XS is in general approximately 1.4 times larger in the abnormal than random seas due to the presence of the abnormal wave in the sea state (as demonstrated in Table 8 for the hogging and sagging significant one-third values). As previously the exponential distribution shows improved agreement with experimental results. We can compare the results for random and abnormal sea states by plotting the probability of exceedence to a base of significant vertical bending moment, as shown in Fig. 17 for each of the sea states. The Rayleigh distribution for each sea state is also shown for comparison. Fig. 17 demonstrates that, whilst the responses deviate from the Rayleigh distribution at x=X S  0:5 in both cases, the probability of exceedence in the abnormal waves is in general higher at the tail of the distribution than for comparable vertical bending moments in random seas; this indicates that the most severe levels of responses appear to be more likely to occur in the abnormal than random seas. The level of severity is dependent on the location on the ship being assessed and the nature of the sea state (either random or abnormal). Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 16. Probability of exceedence of vertical bending moment at (a,b) the forward quarter, (c,d) midships and (e,f) the aft quarter in (a,c,e) random seas and (b,d,f) abnormal seas from experimental results, compared to the Rayleigh distribution and exponential distribution.

4. Comparison to design rules The experimental results were compared to ship design rules to assess whether abnormal waves pose risks beyond those currently considered. Initial comparisons were made as follows: 1. Lloyd's Register (LR) Design Rules for the Classification of Naval Ships (Lloyd's Register, 2012). 2. Det Norske Veritas (DNV) Rules for the Classification of High Speed, Light Craft, and Naval Surface Craft (Det Norske Veritas, 2012). 3. Bureau Veritas (BV) Rules for the Classification of Naval Ships (Bureau Veritas, 2011). Fig. 18 presents the vertical bending moment distributions along the ship, calculated using the specified design rules. Comparisons are made to experimental results in abnormal seas. Exceedence factors for each set of design rules and sea state are presented in Tables 10–12, where the exceedence factor was defined for the purpose of this research as f¼

M expt ; Mrules

ð7Þ

where Mrules is the maximum bending moment derived from the design rules and Mexpt the maximum vertical bending moment measured in abnormal waves. In these tables, cases where the rules values are clearly exceeded (i.e. f41.0) are shown in bold, whilst marginal cases (f E1.0) are in italics. Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 17. Probability of exceedence of vertical bending moment at (a) the forward quarter, (b) midships and (c) the aft quarter in random and abnormal seas, plotted to a base of significant vertical bending moment in MNm.

In general the experimental results at the forward quarter and amidships locations are within the ship design rules. The LR and BV rules appear to provide a greater safety margin than the DNV rules in the hogging (positive) condition, but the reverse is the case in the sagging (negative) condition. The rules values are exceeded at the aft quarter (in both the hogging and sagging conditions) in all sea conditions, as well as in the hogging condition along the length of the ship in Southern Ocean conditions. To attempt to account for these differences, the experimental results were further compared as follows: 1. LR Design Rules for the Classification of Naval Ships including an allowance for extreme waves (Lloyd's Register, 2012). 2. BV Rules for the Classification of Naval Ships including an allowance for bow flare (Bureau Veritas, 2011). It should be noted that the BV correction for bow flare is in the sagging direction only, as it will not occur in hogging. The results of these comparisons are shown in Fig. 19, with exceedence factors in Tables 10–12. The LR extreme wave rules provide a significant safety margin on the experimental values at the forward quarter and amidships, for both the North and South Atlantic conditions in the hogging condition, and all sea states in the sagging condition. These rules provide a closer estimate of the experimental vertical bending moments in some sea conditions in the aft quarter. However, the Southern Ocean experimental values are still well outside of the rules values in the hogging condition along the ship length, as well as the sagging condition at the aft quarter. The BV bow flare rules, as previously stated, do not result in any change in rules values in the hogging condition due to flare slamming not occurring when hogging. They provide a larger safety margin in the sagging condition in the forward half of the ship (as expected to be required if bow flare slamming is occurring and increasing the magnitude of the ship response at the bow) but less so in the aft quarter. Overall it is considered that the BV rules do not necessarily offer any improvement over the LR extreme wave rules. Whilst it is noted that the hogging bending moment in the most severe sea state (Southern Ocean conditions) is well in excess of the design rules, it should be noted that throughout experiments the model was tested at its service speed of 18 knots. This may be an unrealistic scenario for a ship travelling in an already severe sea state and should be considered when Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 18. VBM distributions from the design rules – comparison to experimental results in abnormal waves (full scale). Table 10 Exceedence factors for VBM values in the South Atlantic, based on experimental results. Rules model

Hogging safety margin, fHOG

Sagging safety margin, fSAG

0.75LOA

0.50LOA

0.25LOA

0.75LOA

0.50LOA

0.25LOA

LR DNV BV

0.85 1.19 0.82

0.65 0.79 0.61

1.56 2.04 1.49

0.64 0.58 0.61

0.79 0.71 0.76

2.08 1.89 2.00

LR extreme BV þ flare

0.60 0.82

0.44 0.61

1.09 1.49

0.44 0.38

0.54 0.47

1.43 2.00

Table 11 Exceedence factors for VBM values in the North Atlantic, based on experimental results. Rules model

Hogging safety margin, fHOG

Sagging safety margin, fSAG

0.75LOA

0.50LOA

0.25LOA

0.75LOA

0.50LOA

0.25LOA

LR DNV BV

0.58 0.80 0.55

0.80 0.99 0.76

1.67 2.22 1.59

0.40 0.36 0.38

0.48 0.43 0.46

1.25 1.12 1.20

LR extreme BV þ flare

0.41 0.55

0.55 0.76

1.18 1.59

0.28 0.24

0.33 0.28

0.86 1.20

Table 12 Exceedence factors for VBM values in the Southern Ocean, based on experimental results. Rules model

Hogging safety margin, fHOG

Sagging safety margin, fSAG

0.75LOA

0.50LOA

0.25LOA

0.75LOA

0.50LOA

0.25LOA

LR DNV BV

2.17 3.03 2.08

2.22 2.78 2.13

4.17 5.56 4.00

0.65 0.58 0.62

1.04 0.93 1.00

2.63 2.38 2.50

LR extreme BV þ flare

1.54 2.08

1.54 2.13

2.94 4.00

0.45 0.39

0.71 0.61

1.82 2.50

assessing whether a further safety factor should be included in the design rules. Rigid model experiments in Bennett et al. (2013) further support this idea, as at high speed the vessel experienced a tunnelling effect as it travelled through particularly large abnormal waves, comparable to those tested in this research, which were considered to be unrealistic motions for the normal operation of a ship. Further investigation of these concepts is required. In addition, the different trends seen in the Southern Ocean results are considered to be because the sea state is already severe prior to the inclusion of an abnormal wave in the sea state. Therefore the response history of the vessel (i.e. memory Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Fig. 19. VBM distributions from the design rules including extreme waves/influence of bow flare – comparison to experimental results in abnormal waves (full scale).

Table 13 Uncertainty in experimental results in regular waves at H/LOA ¼ 0.05. ω (rad/s)

Uη (%)

Uζ (%)

Uθ (%)

UM,

6.28 5.23 4.49 3.93 3.49

3.21 2.17 4.45 2.82 0.95

8.39 0.73 3.23 1.70 0.63

9.43 2.67 11.18 0.90 1.61

3.73 3.53 15.26 11.31 4.79

0.75L

(%)

UM,

0.50L

4.08 8.35 5.18 4.66 3.82

(%)

UM,

0.25L

(%)

3.29 3.81 4.75 3.16 5.03

effect) will contribute more to the total response in the abnormal wave due to the more severe sea state encountered prior to the abnormal wave (as discussed in Bennett et al. (2013)) than in the South and North Atlantic conditions. This comparison has been conducted for one representative abnormal wave embedded in a range of random sea states and demonstrates that there may be a deficiency in the design rules when dealing with abnormal wave encounters. Future work will conduct further investigation into the phenomena observed, using a wider range of sea states and abnormal wave heights. 5. Uncertainties Uncertainties in experimental results were calculated using the method of Coleman and Steele (1999) assuming a 95% confidence interval and with uncertainties calculated from the results of three repeat tests. Table 13 presents the total uncertainty in wave profile (Uη), heave (Uζ), pitch (Uθ) and vertical bending moment (UM,0.25L; UM,0.50L; UM,0.75L) in each regular wave frequency tested (model scale), for a representative wave steepness of H/LOA ¼0.05. In general, results show an uncertainty of less than 5% – these levels were consistent across the three values of H/LOA tested. The worst case scenario, where uncertainty levels are close to or greater than 5%, corresponds to the resonant peak of the RAO curves. Table 14 presents the uncertainty analysis for the maximum wave heights and responses in the abnormal seas, again assuming a 95% confidence interval and calculating uncertainties from three repeat tests. In general uncertainties are less than 10%. 6. Conclusions The purpose of this study was an experimental investigation of the global wave-induced loads experienced by a naval frigate in abnormal waves. The experimental results are compared to the design rules to assess whether encountering abnormal waves is sufficiently accounted for. An uncertainty analysis demonstrates a 95% confidence that uncertainties in experimental results are less than 5% in regular waves and 10% in abnormal seas. The encounter with an abnormal wave increases the maximum vertical bending moments by 1.2–2.5 times, compared to the equivalent random seas, for maximum values. Further analysis shows that the significant one-third and one-tenth vertical bending moments also increase when an abnormal wave is introduced, by 1.2–2.3 times and 1.5–3.3 times in the hogging direction respectively, and 1.1–1.9 and 1.2–1.6 times in the sagging direction. These significant increases due to the presence of an abnormal wave may have severe implications when assessing the ability of the design rules to encompass the risks associated with abnormal waves. Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i

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Table 14 Uncertainty in experimental results – maximum responses in abnormal seas. Sea state

Uη (%)

Uζ (%)

Uθ (%)

UM,

1 2 3

8.93 11.55 4.76

9.79 7.43 0.52

7.41 3.71 2.76

3.73 5.94 6.85

0.75L

(%)

UM,

0.50L

3.99 5.84 5.65

(%)

UM,

0.25L

(%)

3.99 5.65 7.96

Results show that the abnormal wave encounter increases the severity of the slamming response with 40–60% of slams having a forefoot emergence of 25%LOA compared to 15–35% in random seas. The maximum vertical bending moment increase with maximum wave height has a linear trend in random seas, but an exponential trend in abnormal waves, demonstrating the importance of the nonlinear response in abnormal seas. Furthermore, experimental results show that, in general, the whipping response is slightly more severe in abnormal than random seas, as demonstrated by the calculated whipping amplification factor. Probability of exceedence calculations show that severe vertical bending moment responses are considerably more likely to occur than otherwise predicted by the Rayleigh distribution. This is the case in the random and abnormal seas, with the experimental distributions by and large deviating from the Rayleigh distribution at vertical bending moments approximately half the significant value in each case. Towards the tail end of the distribution the probability of exceedence in abnormal seas is generally larger than that for comparable vertical bending moments in the equivalent random sea, indicating more severe responses will occur more often in abnormal waves. This is also the case for the rigid body heave and pitch motions, where exceedence probabilities agree reasonably well with the Rayleigh distribution for random seas, but deviate at higher magnitudes of heave and pitch for the abnormal seas. Improved agreement with experimental probabilities is obtained by using an exponential distribution. Comparison to the ship design rules show that in order to have an appropriate safety margin, design rules that account for extreme waves should be used. However, it appears marginal as to whether the design rules are sufficient for vertical bending moments measured towards the stern of the vessel. Furthermore it appears that the hogging bending moments in the most severe abnormal sea are not within the design rule values when travelling at the service speed. However, an allowance here should be included for the actual operational speed of the vessel in a severe sea state, which is likely to be lower than the service speed. This is something that requires further investigation. Future work will use experimental results presented here for validation of a numerical hydroelastic model that can be used for design purposes for abnormal waves. In additional, whilst vertical bending moments appear to be of importance in abnormal waves, the influence of torsion and antisymmetric loading should also be investigated.

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Please cite this article as: Bennett, S.S., et al., Global wave-induced loads in abnormal waves: Comparison between experimental results and classification society rules. Journal of Fluids and Structures (2014), http://dx.doi.org/10.1016/j. jfluidstructs.2014.05.009i