Numerical Study on Effectiveness of Cross-Flooding Device with Different Compartment Arrangements

Zhenghao Liu1, Jianing Li2, Yue Ding2, Decheng Wan1*

1 State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai, China

2 Shanghai Waigaoqiao Shipbuilding Co., Ltd, Shanghai, China *Corresponding author

ABSTRACT When a ship is damaged, seawater floods into the damaged ship and may seriously threat the safety of passengers and crew. Cross-flooding device can be used to reduce the heeling of a damaged ship. We use the in-house CFD solver naoe-FOAM-SJTU to simulate the flooding process of a ship with symmetric and asymmetric compartments. The relationship between the compartment arrangement and the water flooding process as well as the ship is presented and discussed. The results show that the present CFD solver can be an alternative tool to deal with water flooding problems. KEY WORDS: Compartment arrangement; cross-flooding device; damaged ship; 6DOF motion INTRODUCTION Large cruise carries a great number of passengers and crews. Maritime accidents such as water floods into the compartment of the ship seriously affect threat the safety of passengers and crew. With the increasing number of ships, the international rules and regulations on damaged stability are becoming stricter. A thorough understanding of dynamic behavior of damaged ships and seawater flooding process is vital for passengers and crews. However, it is very difficult to assess the stability of damaged ship because the ship’s motion is highly coupled with water flooding and water sloshing in the compartment. Previous investigations of water flooding problems were mainly carried out by model test and numerical simulation. Model tests were generally designed to investigate the influence of damage size and longitudinal bulkheads in the flooding behavior of the ship. Although model test cannot deal with this problem efficiently, experimental data is essential for CFD validation. Many researchers use both model test and numerical simulation to study the damaged ship stability. Santos et al. (2002) studied the transient asymmetric flooding of a Ro-Ro shaped barge in calm water using theoretical simulation and experimental work. The experimental and theoretical results suggest that further

experimental investigations are necessary in order to calibrate the theoretical model and refine the modelling of the flooding process. Palazzi and Kat (2004) used a flooding model to study the motion behavior of a damaged frigate in calm water and in waves. They found that air-flow effects may result in extra roll damping, and computed roll motions in waves get closer to the test results. They also found that calculations overestimate the transient maximum roll angle, which is related to an overestimation of the inflow inside the small wing tank and to a potential momentary sloshing inside the forward compartment. Cho et al. (2006) conducted a series of numerical and experimental studies for the damaged part of ITTC RO-RO passenger. They used FLOW3D to simulate the motion and hydrodynamics of the damaged passenger and found both the motion and forces on the model agreed reasonably well with experiments. Lee et al. (2012) performed a series of free roll decay tests in calm water with both intact and damaged conditions. The 6DOF motion of the model was measured in regular waves with intact condition. They established database that provides 6DOF motion responses of intact ship and investigated the effects of the flooding water on the roll decay motion of a ship. Rodrigues et al. (2018) conducted both experimental and numerical investigation of the partial flooding of a barge model. The discharge coefficient at different opening geometries in calm water from pressure measurements in flooding compartments. Nowadays, CFD method has been widely used in the field of marine and ocean engineering. It can be used to simulate complex water flooding problems and can provide fine flow information. Gao et al. (2004) used coupled FLUENT and potential flow solvers to simulate damaged ship flooding. Inside the model and in the model’s vicinity, the FLUENT is adopted. The far field flow is solved by the potential flow solver. They found that the calculated hydrodynamic forces agree well with experimental measurement and the water flooding process can be evaluate numerically. Gao and Vassalos (2012) conducted numerical study of damage ship hydrodynamics. Skaar et al. (2006) used a smoothed particle hydrodynamics (SPH) method for modelling the flooding of a 2D section of a RO-RO ship with forced heave and roll motions in regular waves. Ruponen et al. (2007, 2010 and 2017) developed a new method for flooding based on the pressure-correction technique. They found that the simulation method can predict

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Proceedings of the Twenty-ninth (2019) International Ocean and Polar Engineering ConferenceHonolulu, Hawaii, USA, June 16-21, 2019Copyright © 2019 by the International Society of Offshore and Polar Engineers (ISOPE)ISBN 978-1 880653 85-2; ISSN 1098-6189

www.isope.org

accurately both the floating position and the water heights in the compartments. Strasser et al. (2009) applied RANS equations for modelling the experiments by Ruponen (2006) of a box-shaped barge flooding. The floodwater dynamics and water flooding through various openings and opening shapes in the ship are accounted. Gao et al. (2013) conducted numerical study of damaged ship flooding in beam seas. Begovic et al. (2015) applied STAR CCM + to predict the roll damping of intact and damaged models of the naval ship hull DTMB 5415. They found that numerical predictions of free roll decay satisfactory agreed with experimental results. Although many researches have been done on water flooding problems, very few attempts have been made to study the effect of compartments arrangement on water flooding. The objective of the present work is to investigate the flooding process of a ship with symmetric and asymmetric compartments. The focus is on the compartment arrangement effect on flooding process. In this paper, present CFD calculations are performed by the in-house CFD solver naoe-FOAM-SJTU. The volume of fluid (VOF) method is applied to capture the flooding process and free surface. 6DOF and dynamic mesh module are used to deal with the ship motion. Laminar is adopted as turbulence model in our simulation. The time histories of several wave gauges in the compartments and near the ship, ship motion and force on the ship are present for both cases. The whole water flooding process is presented and discussed. Detailed flow information in the compartments and near the ship are also given. The paper is organized as follows: next section presents the numerical methods including governing equations, volume of fluid (VOF) method, dynamic mesh deformation and discretization schemes; after that we describe the details of numerical model; in the next part, the compartment arrangement effect on flooding process is discussed; finally, some conclusions of this work are drawn. NUMERICAL METHODS

Governing Equations The CFD solver naoe-FOAM-SJTU is based on the open source platform OpenFOAM and designed for the application in marine and ocean engineering field (Shen et al., 2015; Wang et al., 2015; Wang and Wan, 2016; Zhao and Wan, 2016; Wang and Wan, 2018; Zhao et al., 2018). The governing equations of incompressible viscous fluids in naoe-FOAM-SJTU solver are as follows:

0∇ ⋅ =U (1)

( ( ) )

( ) ( )tp x f fσ

ρ ρ

ρ μ μ

∂ + ∇ ⋅ − =∂

−∇ − ⋅ ∇ + ∇ ⋅ ∇ + ∇ ⋅ ∇ + +d eff eff s

U U U U

g U U

ɡ (2)

where U and Ug are the velocity field and the velocity of grid nodes, respectively. pd is the dynamic pressure and p is the total pressure, ρ is the mixed density of the two phases water and air. μeff is the effective dynamic viscosity, in which 𝜈 and 𝜈t are kinematic viscosity and eddy viscosity, respectively. fσ is the surface tension, which impacts the free surface. fs is a source term, added to generate the sponge layer for wave absorbing.

VOF Method VOF method (Hirt and Nichols, 1981) with artificial bounded compression techniques is adopted in naoe-FOAM-SJTU solver to

capture the free surface and the water flooding process. The interface between the two phases is determined by introduction of an advection equation:

[( ) ] [ (1 ) ] 0tα α α α∂ + ∇ ⋅ − + ∇ ⋅ − =

∂ ɡ rU U U (3)

where 𝛼 is the volume fraction. For an interface cell, the value of volume fraction α is between 0 and 1, representing it contains both water and air.

=0 air=1 water

0 1 interface

αα

α

< <

(4)

In physical domain, the density of fluid ρ and the dynamic viscosity μ can be obtained by a weighted value based on the volume fraction α:

1 2(1 )ρ αρ α ρ= + − (5)

1 2(1 )μ αμ α μ= + − (6) Where ρ1 and ρ2denote the density of water and air, μ1 and μ2 denote the viscosity coefficient of water and air, respectively.

Dynamic Mesh Deformation In this study, the dynamic mesh technique is applied for ship motion, which can keep the topology of the mesh unchanged during the simulation. The mesh velocity is determined by solving Laplace’s equation at each time step, and the new positions of the vertices of the mesh can therefore be obtained.

( ) 0gUγ∇ ⋅ ∇ = (7)

Where 2

1r

γ = is the quadratic inverse distance of cell center to the

nearest moving wall boundary. Ug is the grid velocity.

Discretization Schemes To discretize the RANS and VOF transport equations in OpenFOAM, the finite volume method (FVM) is adopted. Van Leer scheme is applied for VOF equation. The merged PISO-SIMPLE algorithm is used to solve the coupled equation of velocity and pressure. The convection terms are solved by a second-order TVD limited linear scheme, and the diffusion terms are approximated by a second-order central difference scheme. GEOMETRY AND TEST CONDITIONS

Numerical Models The numerical model chosen in this work is a damaged ship. The geometry includes two empty compartments, a rectangular damaged opening and 5 pipes connecting the two compartments, shown in Fig. 1. For the main parameters of the ship are confidential, they are not presented in our work. The length of the ship is about 300 meters. The center of gravity of the ship is located at (8 m, 0 m, 10.7 m) in the earth coordinate. In the starboard side of the ship, there is a rectangular opening with a length of 7 m and height of 2 m. The center of the opening is (-48.5 m, 18.6 m, -1 m).

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Fig. 1 Damaged ship model Symmetry and asymmetry compartment arrangements are adopted in this work, as shown in Fig. 2. For the starboard side compartment, the length is 21 m (x= -59 m ~ -38 m), the width is 17.6 m (y= -1 m ~ -18.6 m) and the height is 5.6 m (z= -2.7 m ~ 2.9 m). For the port side one, only location in x direction changed. For symmetry case, x ranges from -59 m to -38 m, which is the same as starboard side one. For asymmetry case, x ranges from -51 m to 30 m. 5 circular cross-flooding pipes with 8 m2 are distributed from x= -49 m to x= -41m. Their positions are shown in Fig. 3.

Fig. 2 Compartment arrangements: symmetry (left) and asymmetry (right)

Fig. 3 Pipes connecting the two compartments Using the CFD solver naoe-FOAM-SJTU, the water floods into a damaged ship can be simulated. According to the length of the ship, the numerical domain was set to -400 m < x < 400 m, -300 m < y < 300 m, -50 m < z < 30 m. The computational domain is shown in Fig. 4.

Fig. 4 Computational domain The background mesh is generated by blockMesh provided by OpenFOAM. An automatic mesh generation tool snappyHexMesh is then applied to split hexahedral cells into split-hex cells and snap to the STL geometry. The mesh around the ship is shown in Fig. 5. The total grid number is about 5 million for both cases. To make it easy to converge in each time step, the interface Courant number was controlled to be under 1. The time step is 0.002s in each case. For the damaged opening and the two compartments, the mesh is refined, as shown in Fig. 6. The boundary conditions are as follows: The inlet, outlet and sidewalls of the computational domain are set as symmetry condition. The atmosphere is set to be pressure outlet so that the air can exit from the domain or enter the domain. The bottom wall, the ship and the compartment use no-slip wall boundary.

Fig. 5 Computational mesh around the ship

Fig. 6 Detail of mesh around opening 9 wave gauges were placed in each compartment to measure the free surface of the flooding water. The positions of the wave gauges for symmetry and asymmetry case are shown in Fig. 7.

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Fig. 7 Layout of wave probes in compartments: symmetry case (left) and asymmetry case (right) RESULTS AND DISCUSSION

Roll motion of the ship At the start time, the ship is placed in the calm water to allow the water floods into the compartment through the damaged opening. Only roll motion is released in our simulation. The simulations of water flooding process run up to 100 s. Fig. 8 shows the results for the ship roll motions for symmetry and asymmetry case. The roll motion is very slow for both cases. This is due to the size of the opening and compartment is relatively small compared with the ship size. So the different arrangement of compartment has little influence on ship motion. As shown in Fig. 8, the trend of roll motion for the two cases are similar at the initial stage. As the water floods into the compartment at the starboard side, the roll motion increases until it reaches maximum value 4.6° at about 56 s. When the water constantly enters the compartment at the port side through the pipes connecting the two compartments, the roll motion will be reduced.

Fig. 8 Time history of the ship roll motion

Water height in the compartments The water height in the starboard and port compartment at several wave gauges are presented in Fig. 9 and Fig. 10 for both cases. The time histories of wave gauges are not smooth curves, which is due to the fact that the flow becomes violent during the flooding process and there is undulation. This phenomenon is more obvious for the WPS1 wave gauge, which is located near the damaged opening. The fluctuation of surface elevations at the starboard side is stronger than those at the port side. This is because that the flow rate at damaged opening is larger than the pipes connecting the two compartments. At 100 s, the surface elevation at the starboard side is close to the calm water outside the ship, while surface elevation at the port side is still lower than calm water.

(a)

(b) Fig. 9 Water elevation of wave gauges in starboard side: (a) symmetry case (b) asymmetry case

(a)

(b) Fig. 10 Water elevation of waves gauges in port side: (a) symmetry case (b) asymmetry case

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T=5s T=15s T=25s

T=50s T=70s T=100s

(a)

T=5s T=15s T=25s

T=50s T=70s T=100s

(b)

Fig. 11 The free surface profiles at different time steps: (a) symmetry case (b) asymmetry case

The free surface profiles are presented in Fig .11 at 6 different time steps for both cases. It could be seen that the water from side opening flush into the starboard compartment very quickly at the initial stage. This is due to the hydrostatic pressure. At this stage, transient phenomena such as breaking water can be found, and the fluctuation of the free surface of the tank can be seen as shown in Fig. 9. The water will move forward along the bulkhead. When the water level in starboard compartment increases, it will flood into the port compartment. At 15 s, the water flooding shows different characteristic. For symmetry case, the water floods towards the center of port compartment, and then diffuse to the bulkhead. For the asymmetry case, the water floods along the bulkhead directly, and there is little water in the center of the port compartment even at 25 s. With the increase of water in the compartments, the free surface shows similar characteristic for both cases. At 50 s, water runs up on bulkhead can be clearly seen.

Fig. 12 shows the velocity distribution in the y-direction at different time steps for both cases. It can be seen that the velocity at the damaged opening has the maximum value. At the initial stage of water flooding, the velocity is larger and water floods to port side rapidly. With the increase of water level, the water velocity in the starboard compartment decreases. When the water hits the port side bulkhead, it will rush upward. The water flow can be relatively complex as shown at 50 s. At 70 s and 100 s, the velocity in both compartments are at low level.

T=5s T=15s T=25s

T=50s T=70s T=100s

(a)

T=5s T=15s T=25s

T=50s T=70s T=100s

(b) Fig. 12 Velocity distribution in the y-direction at different time steps: (a) symmetry case (b) asymmetry case

Calculated forces and moments on the ship The water floods into a damaged ship will affect the motion and the hydrodynamic force on the ship. Fig. 13 and Fig. 14 show time histories of y-direction force and z-direction force, respectively. We can see that the y-direction force increases with time and then decreases after 56 s. The fluctuation becomes larger between 20 s and 56 s. As the amount of water in the compartment increases, the water flows on the wall of the compartment and collides with each other. The flow in the compartment becomes violent during this process. Thus, the fluctuation increases. After 56 s, the water level at the starboard almost reaches the calm water and the roll motion decreases. The ship tends to be stable. Thus, the fluctuation of y-direction force decreases for both cases. As we know, the z-direction force is caused by the water floods into the compartment, which can reflect the flow rate through the damaged opening. It can be noted that the z-direction forces are almost the same for the two cases, which indicates that the flow rate of the two cases keeps the same. Fig. 15 shows the comparison of time history for roll moments for both cases. It can be seen that the moments increase from 0 to 100 s and the moments for asymmetry case is smaller than the symmetry case after 40 s.

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Fig. 13 Comparison of time history for y-direction force

Fig. 14 Comparison of time history for z-direction force

Fig. 15 Comparison of time history for roll moments

CONCLUSIONS In this work, the in-house naoe-FOAM-SJTU solver is adopted to investigate the flooding process of a ship with different compartment arrangements. The whole water flooding process for symmetry and asymmetry case is captured by VOF method. The ship motion, the hydrodynamic force, the free surface elevation in the compartments and the velocity fields are presented. As the size of compartment and damaged opening is relatively small compared to the ship, the symmetry or asymmetry arrangement of compartments has little effect on the motion or hydrodynamic force of the ship. However, the different compartment arrangements have great influence on the water flooding process at the port side compartment. Further work should be focused on comparison of quantitative data such as pressure distribution, velocity distribution, free surface profile, resultant force

and moment between numerical simulation and experimental results. ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (51879159, 51490675, 11432009, 51579145), Chang Jiang Scholars Program (T2014099), Shanghai Excellent Academic Leaders Program (17XD1402300), Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning (2013022), Innovative Special Project of Numerical Tank of Ministry of Industry and Information Technology of China (2016-23/09) and Lloyd’s Register Foundation for doctoral student, to which the authors are most grateful. REFERENCES Begovic, E, Day, AH, Incecik, A, Mancini, and Pizzirusso, D (2015).

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