Keywords

1 Introduction

Ship accidents may occur due to various reasons; collision, running a ground, malfunctioning of an engine, attack, etc. When a ship is damaged for certain reason, she loses her function and safety. So, the evaluation of the motions and assessment of stability is very important. Many efforts have been also made for the development of numerical methods for the behaviour of damaged ship . These numerical methods have been validated and improved by the international benchmark studies such as those done by ITTC and HARDER project. Up to now it is believed that the numerical methods are able to predict the overall tendency of the damaged ship motions and flooding process to an extent compared with experiments. But reliable prediction is difficult because the underlying phenomena are very complicated and highly nonlinear due to the various factors such as geometry of damaged compartment, flooding process and waves etc. To improve the accuracy of the numerical methods and the understanding of the mechanism of flooding process, data of various damaged scenarios need more thorough numerical simulations and experiments. Also it is generally believed that the physics of damaged ship can be analyzed by experiments more realistically.

In this study a series of experiments and numerical analyses have been carried out for the behaviour of a damaged cruiser in waves. Two damaged configurations are selected to study the damage effects. The one is the mid-section part which has 6 compartments. The second is the fore-section part which has 4 compartments. The starboards of hull are damaged for two damage conditions. The flooding tests were performed for the transient process and the flood water height was measured by 19 water height sensors. To study the effect of flood water and damage compartment, model tests were carried out in various wave conditions. The motion tests in waves were carried out after the compartments are completely flooded. The experiments indicate that the internal compartment influences the transient flooding process and roll motion. When there is water with free surface in compartments and the ship moves at the natural frequency of internal water in the compartment, coupling of internal water and ship motion occurs. The numerical simulations were conducted using quasi-static model, quasi-dynamic model and CFD. The quasi-dynamic model adopts the mass-spring for internal water motion description. The model considers the dynamics of free surface as ship motion. This mass-spring equation is explicitly coupled with ship motion equation. The quasi-dynamic model shows the intermediate results of CFD and quasi-static model.

2 Model Experiment

The model tests were performed in KRISO ocean engineering basin (L × B × D: 56 × 30 × 4.5 m). The model ship is a cruiser and the hull data of cruiser is provided by SSRC. The contents of model test are as follows.

  • Motion in regular and irregular waves

    Intact, damaged conditions

  • Flooding process in calm water

    Intact, damaged conditions

  • Free decay in calm water

    Intact, damaged (opened, closed)

2.1 Ship Model

The object ship is a cruiser. The main particulars are summarized in Table 13.1 and Figs. 13.1 and 13.2 show lines and model of the cruiser. The model was fitted with bilge keels. Its length is 75 m and height is 0.50 m in prototype. They are symmetrically located about the mid ship at half the bilge girth. The inclination with the vertical is 45°. The model was around 5 m long corresponding to a scale of 50.

Table 13.1 Particulars of cruiser
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Fig. 13.1
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Lines of cruiser

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Fig. 13.2
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Cruiser model

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2.2 Damage Compartment

Two damaged scenarios were chosen. The one (DAM1) is that mid-section part is damaged, which has 6 compartments. The second (DAM2) is that fore section part is damaged, which has 4 compartments. These damaged parts are little different with the original inner compartment of the cruiser. The compartments were simplified for model tests. The inlet of damaged compartment is located at the starboard side, the length is 6 m and the height is 5 m. The general arrangements of the damaged compartment are shown in Fig. 13.3.

Fig. 13.3
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Arrangement of damage compartments (CP10/11, CP17)

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The damage models are shown in Fig. 13.4. The material of the damaged model is acryl and thickness is 5 mm. The coordinates of compartments and inner connections can be found in Cho et al. (2009) . The origin is amidships (10 St.) in x, center in y and baseline in z direction. The inlet of DAM1 is from 3.4 to 8.4 m from baseline and the top of inlet is above the water free surface. The top of DAM2 inlet is 8.05 m from the keel. The inlet is opened by pulling the door suddenly during model test.

Fig. 13.4
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Damage compartment model

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2.3 Environmental Conditions

The characteristics of damaged cruiser in waves are investigated. To study the effects of flood water and in/out flow through damage inlet, motions of cruiser and flooding heights in compartments are measured. In order to study the effects of wave height on the roll RAO, 4 regular wave heights (1, 3, 5, 7 m) are used. The wave conditions are as follows.

  • Regular waves

    Frequency: 0.2–1.1 rad/s

    Height: 1, 3, 5, 7 m

  • Irregular waves: JONSWAP (gamma = 3.3)

    Irregular wave 1: H1/3 = 1 m, Tp = 5sqrt(H1/3)

    Irregular wave 1: H1/3 = 3 m, Tp = 5sqrt(H1/3)

2.4 Measurement System

To analyze the behaviour of damaged ship , the motions of the ship and water in compartment must be measured. The 6 dof motion of ship are measured by non-contact optical system (RODYM6D). The flooding flows in each compartment are measured by capacity type wave probes. The number of wave probe is 10 in CP10/11 and 6 in CP17. Video cameras are also used to record the flooding process. The RBM1 is in CP10-R1S next to damage inlet (Fig. 13.5). The locations of wave probes can be found in Cho et al. (2009) .

Fig. 13.5
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Locations of flooding height sensor

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3 Numerical Method

In order to analyze the flooding numerically, the quasi-static model (Cho et al. 2009) and quasi-dynamic model are used. The quasi-dynamic model is lumped mass-spring system. This model calculates the free surface angle with respect to the horizontal plane while the ship moves. Figure 13.6 shows the concept of quasi-static and quasi-dynamic model. The quasi-dynamic model equation coupled with ship motion is solved. The 4th order Runge-Kutta method is used for time integration.

$$a_{1} \dddot y + a_{2} \dot{y} + a_{3} y = - b_{1} \ddot{x} - b_{3} x$$
(13.1)

where y is free surface angle, x ship roll, a and b equation coefficients.

$${\text{v}}\,{ = }\,\dot{y}$$
$$\dot{v} = \frac{{ - b_{1} \ddot{x} - b_{3} x - a_{2} v - a_{3} y}}{{a_{1} }}$$
(13.2)
Fig. 13.6
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Free surface description for quasi model

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4 Test Results and Discussion

4.1 Experimental Results

4.1.1 Free Decay Test

Figure 13.7 shows the results of roll free decay test. The natural roll period of intact ship is 21 s. The period of DAM1 decreases to 19.8 s because of flooding , heeling and free surface, etc. When the inlet is closed after flooding, there is no in/out flows though the inlet and the period of DAM1 for closed inlet is 20.8 s. The period of DAM2 is almost the same as intact ship. The equivalent damping values are plotted in Fig. 13.7. The damping values of intact and DAM2 range from 2 to 4%. The damping values of DAM1 increase from 4 to 6% (Table 13.2). The damping value of DAM1 is proportional to the magnitude of initial angle. When inlet is opened, flooding starts at the starboard side and water accumulates much more at the starboard side then the ship heels to the right. After flooding , roll is not symmetric and the roll and damping is not symmetric anymore. There is flow in/out through the CP10-R1S during free decay of DAM1. This indicates that the estimation of damping is difficult when a damaged part is severe. In case of the closed condition, there is no flow in/out through opening. The roll is affected by only internal water motion. The natural periods are very similar but the damping of DAM1 increases due to the flooding water motion.

Fig. 13.7
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Results of free decay

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Table 13.2 Initial roll angles and equivalent damping values of free decay test
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4.1.2 Flooding Test in Calm Water

The flooding test was performed in calm water for DAM1 and DAM2. Figures 13.8 and 13.9 shows the height of flooding water compartments and motions. The flooding through the inlet starts at CP10-R1S (RBM1) and continues to CP10-R1C (RBM2, 3, 4) and CP10-R1P(RBM5). The water instantly fills up CP10-R1S. After filling of CP10-R1S, water propagates to next compartments. The RBM6, 7 and 8 show the flow from CP10 to CP11. The required time for flooding of second floor, CP10/11-R2 is about 240 s. Figure 13.9 shows the motions with flooding. Roll motion begins at the same time with flooding and reaches the steady state (~400 s) after filling of CP10-R1S/C/P. The flooding process of DAM2 is quite simple due to simple geometry and configuration. The flooding starts at CP17-R1 and flooding water reaches to the bottom of CP17-R2.

Fig. 13.8
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Height of flooding water in DAM1 compartments

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Fig. 13.9
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Motions of ship with flooding of DAM1

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4.1.3 Tests in Waves

The motion tests in waves were carried out in the condition that the compartments were flooded. This gives the same initial condition in different waves. The results of motions in waves are shown in Figs. 13.10, 13.11 and 13.12. The wave amplitudes of regular wave are 1, 3, 5, 7 m to investigate the effect of nonlinearity of the incident waves on the roll motion. The roll motions are significantly influenced by wave amplitude and damage conditions. Interestingly enough, the effect of wave amplitude on roll motion also appears in intact condition. The peak value of roll RAO decreases at resonance frequency when wave amplitude increases. In case of DAM1, roll RAOs are changed due to internal water motion and inflow/outflow. The resonance frequency moved from 0.3 to 0.33 rad/s due to sloshing . The effect of internal water motion appears for wave amplitude 3, 5, 7 m and sloshing occurred in CP10/11-R2. This is sloshing in low filling ratio. When wave amplitude is 1 m, the internal water motion is small and sloshing doesn’t occur. In order to excite sloshing in a considerable level, waves more than 3 m should be incident because the ship heels 4° to starboard. Figure 13.13 shows the effect of opening and in/outflow. The difference between open and close may be explained by the magnitude of sloshing effect. In case of close condition, the effect of sloshing is strong. When inlet is opened, sloshing is weakened because the damping increase due to in/out flow. In case of DAM2, roll RAOs is similar with intact RAOs. Although sloshing in CP17-R2 occurs, there is no significant influence of flooding because of small amount of water.

Fig. 13.10
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Roll RAO of intact

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Fig. 13.11
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Roll RAO of DAM1

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Fig. 13.12
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Roll RAO of DAM2

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Fig. 13.13
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Effect of opening on the roll motion (DAM1, ω = 0.33 rad/s)

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Figures 13.14, 13.15, and 13.16 show the roll motion and internal water motion in CP10/11-R2 for the condition of wave frequency 0.30 and 0.33 rad/s. The position of water height measurement (RBM9/10) is at the center in compartments. The initial value of water height is zero in flooded situation. The positive value stands for increasing and negative value decreasing. When wave height is 1 m, flooding water doesn’t reach to port side wall and sloshing doesn’t occur. But in case of wave height 5 m, flooding water reached port side wall. When wave frequency is 0.33 rad/s, the coupling of sloshing and roll is more strong. Table 13.3 shows the phase of roll and incoming wave due to sloshing (Figs. 13.17 and 13.18).

Fig. 13.14
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Motion and flooding of DAM1 (Regular wave test, A 1 m, ω 0.3 rad/s)

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Fig. 13.15
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Motion and flooding of DAM1 (Regular wave test, A 5 m, ω 0.3 rad/s)

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Fig. 13.16
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Motion and flooding of DAM1 (Regular wave test, A 5 m, ω 0.33 rad/s)

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Table 13.3 Phase of wave and roll
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Fig. 13.17
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PSD of intact in irregular wave (Hs 3 m)

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Fig. 13.18
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PSD of DAM1 in irregular wave (Hs 3 m)

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4.2 Numerical Simulation Results

Figures 13.19, 13.20, 13.21, 13.22 and 13.23 show the simulation results for ITTC tanker model. The model test results were from MARIN, Surship3 is KRISO results using quasi-dynamic model, and Coupled cal. stands for viscous CFD results. The free decay results of quasi-dynamic model are similar with experiments and CFD. This indicates that the quasi-dynamic model can calculate the dynamics of free surface. Also regular wave test shows the reasonable results. The merit of quasi-dynamic model is very fast calculation in comparison to viscous CFD. The required time is almost same as quasi-static model.

Fig. 13.19
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Free decay (h = 0 m)

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Fig. 13.20
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Free decay-sub resonance (h = 3 m)

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Fig. 13.21
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Free decay-resonance (h = 4 m)

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Fig. 13.22
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Free decay-non-resonance (h = 16 m)

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Fig. 13.23
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Roll RAO-non-resonance (h = 4 m)

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The damaged problem is calculated by the quasi-dynamic model. The results are shown in Figs. 13.24, 13.25, 13.26, 13.27 and 13.28. The transient flooding process is well represented by the model. The flooding heights are compared and the numerical results agree with experiments. But the calculated roll is different. This may be due to the different amount of flooding water in CP10R1S. The increase of numerical result in CP10R1S is almost step jump to saturation limit and CP10R1S is full. But experiment shows CP10R1S is not filled once and is full after 150 s. This lag may be occurred due to the air compression and numerical model limit. Figures 13.27 and 13.28 show the regular wave results. Roll RAOs show similar tendency of experiments. The viscous CFD calculation (Figs. 13.29 and 13.30) shows very similar results also.

Fig. 13.24
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Roll free decay of cruiser

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Fig. 13.25
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Comparison of flooding heights for DAM1

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Fig. 13.26
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Comparison of motions for DAM1

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Fig. 13.27
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Roll RAO for intact and DAM1—Quasi-dynamic model

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Fig. 13.28
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Roll RAO comparison for DAM1—Quasi-dynamic model

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Fig. 13.29
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CFD Mesh for viscous simulation

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Fig. 13.30
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CFD calculation of flooding height for DAM1

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5 Conclusions

The experiments and numerical analysis have been performed for investigating the behaviour of damaged cruiser in waves. The influences of damage configuration, internal water motion, wave height and flow in/out are considered. The transient process and motion behaviour in waves are analyzed. The transient flooding process is measured in each compartment. The effect of flooding on the ship motion appeared in roll motion. Although the amount of water in the upper compartment is small, sloshing is occurred and the effect is significant. Quasi-dynamic model and viscous CFD shows quite good results. The physics and phenomena are more explained and understood by both the experiment and numerical analysis.