Fluid structure interaction analysis of a ship collision

Transcription

1 Proceedings of the ICCGS June, 2016 University of Ulsan, Ulsan, Korea Fluid structure interaction analysis of a ship collision Smiljko Rudan 1), Davor Volarić 1) 1) Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Croatia Abstract Ship collisions are marine accidents in which, during the impact, a significant amount of the kinetic energy is used for the deformation and destruction of the colliding ships structural members. Depending on the collision scenario, a part of the impact energy is also used in the generation of the hydrodynamic effects, namely the drag force effects and the generation of waves. Classic approach to the analysis of ship collision problems is to account the hydrodynamic effects within the global motion or external dynamic analysis, while restraining the local deformation analysis to the internal mechanics analysis. Current state-of-the-art collision analysis couples both the external dynamics and internal mechanics through the nonlinear FEM analysis of complex models. However, hydrodynamic effects are either neglected or taken into account in a simplified manner. This paper aims to address the modeling and analysis issues of a fluid-structure interaction (FSI) type of ship collision analysis. A hybrid struck ship model, consisting of a structural model and a fluid model, is generated with a twofold purpose: to assure realistic collision simulation and, at the same time, to enable, as much as possible, the insight into the collision hydrodynamics. Fully coupled, long-term FSI analysis is performed using LS-Dyna commercial code and a discussion on the findings and results are presented. Keywords Ship collision, Fluid-Structure Interaction (FSI), Arbitrary Lagrangian-Eulerian (ALE) method Introduction Ship collisions are marine incidents where a ship collides with another ship, offshore object, floating objects such as icebergs or lost containers etc. Within this article only collision between two ships will be considered. In that case, a striking ship is a ship that collides with the struck ship and during the collision a combined kinetic energy of both ships is transformed into elastic and plastic deformation energy of ship structures, a change of both ships speed, heading and motion in general, as well as for the generation of the liquids motion such as sloshing of liquid cargo in the tanks or movement of the surrounding water. A significant amount of research is performed when elastic and, more importantly, plastic damage of both striking and struck ship structures are in concern, see e.g. Ozguc et al. (2005) and Pedersen (2010). Due to the careful theoretical analysis, advancement of the calculation power and sophistication of the software, numerous experiments performed and a close look to a number of parameters affecting collision, reliable simulations of ship collision were successfully performed. However, the accuracy of such collisions still has to be carefully validated having in mind that each collision event is a unique event. Certain amount of research is performed in the attempt to understand the effects of liquid motion in collision. It has been proven that liquid cargo sloshing in a partially filled tanks having damping effects i.e. liquid sloshing overtakes a part of collision energy and therefore structural damage is reduced, see e.g. Zhang & Suzuki (2007), Tabri et al. (2009) and Rudan et al. (2010). Some attempts are being made to take into account the global motion of the ships in collision and to study the effect of drag force induced mostly by side movement of the struck ship, Rudan & Aščić (2014). Finally, considering the movement of the striking and struck ships in the water only a limited amount of research was performed. The reason for that is a complexity of the collision event. The realistic simulation should take into account both structural damage and fluidstructure interaction (FSI) during the whole duration of the event. Gagnon & Wang (2012) presented the results of the numerical simulation of tanker collision with a bergy bit. Lee at al. (2013) presented various examples of complex FSI ship collision and grounding analysis, however, they provided very little information about the control of the analysis parameters, fluid properties etc. The purpose of this article is to present an attempt to perform the fully coupled, long-term FSI analysis using LS-Dyna commercial code. FSI Analysis Fluid-structure-interaction analysis considers the coupling of Lagrangian and Eulerian domain in the same analysis model. Several concepts are combined in commercial software packages, such as LS-Dyna, to accom-

2 plish that. First one is the Arbitrary Lagrangian-Eulerian (ALE) formulation where, as the name of the method indicates, Lagrangian and Eulerian steps are successively applied with the advection steps in-between. When compared to the Eulerian method, the remapping of the nodes in ALE method is not restricted to the starting nodes positions. The second is Multi-material Euler/ALE formulation where several materials can be mixed together in the same fixed mesh. Finally, an FSI algorithm is defined which couples the Eulerian, Lagrangian and single or multi-material ALE parts within a single analysis model. In LS-Dyna both penalty and constraint based method is used for controlling the fluid structure relationship. LS-Dyna software package provides tools for setting up and controlling the FSI analysis and one such analysis will be presented. Multi-material ALE (MM-ALE) formulation is used to define a fluid environment consisting of water and air in arbitrary mixture within a single element. Constrained-Lagrange-in-Solid formulation was used to control the relation between a Lagrangian ship structures and MM-ALE domain. Collision scenario In the collision scenario considered in this article two similar size ships will collide. Particularly, a ferry will hit an LPG tanker amidships, at the right angle (i.e. orthogonally), with a speed of 8 m/s. This collision scenario may be considered realistic for the routes where cargo and passenger traffic is crossing, as it is the case in e.g. Baltic or Adriatic Sea. In the Baltic Sea the cargo traffic, including tankers, occurs mostly in the west-east direction, connecting the east ports with the ocean on the west. At the same time, significant amount of the ferry traffic occurs in the north-south direction, connecting Scandinavian countries with the south Baltic countries. In a similar way, in the Adriatic Sea, most of the cargo traffic occurs in the south-north direction, connecting the mid Europe ports in Trieste, Kopar and Rijeka, among others, to the Sues Chanel or Gibraltar merchant routes. At the same time, there exists an Adriatic west-east route for a number of cargo, passenger and leisure traffic. Table 1 lists the particulars of the ships in collision. Struck ship is a type C tank LPG ship having a single hull in which two tanks for LPG cargo resides. Type C tanks are independent vessels of cylindrical and bi-lobe design subjected to pressure and low temperature in order to keep cargo liquefied. Striking ship is a ferry of the size and design typical for Croatia ferry fleet. Sailing speed of a ferry is 8 m/s and at such a speed a collision will occur. Struck ship model Struck ship model is generated using FEMAP with NX Nastran software package and later on translated into LS-Dyna input deck. The struck ship finite element model is presented on Figure 1. The model consists of coarse mesh rigid parts and fine mesh elastic-plastic parts. The aft and fore parts of the model are modeled as rigid structures representing aft and fore parts of the hull. The mass of these parts is concentrated into single mass elements and adequately linked to corresponding hull parts. Table 1: Two ship in collision particulars Parameters LPG ship Ferry Length over all m Ship weight 3607 t 5757 t Mass of the cargo t 6889 t Displacement(at 1.025t/m3) t 6889 t Draft aft 4.85 m 5.25 m Draft fore 4.59 m 5.30 m Middle draft 4.71 m 5.28 m Center of gravity height 4.31 m m Center of gravity length m m The amidships is modeled with both coarse and fine mesh elements. Fine mesh elements, including some coarser mesh elements in the transition zone, are modeled as elastic-plastic structure. The rest of the amidships is modeled with coarse mesh and is considered rigid. Figure 1: FE model of a struck ship (up) and typical transition from the fine mesh to the coarse mesh in the cargo hold (down) A large portion of the entire model is therefore rigid which is an assumption applied in the attempt to keep the calculation time within reasonable limits. However, out of the previous analysis it was found that fine mesh zone will accept all the collision damage and nearly all elastic deformation. More details about the struck ship model can be found in (Rudan et al. 2013). In addition to the mentioned finite element mesh, an additional lightweight rigid structure is imposed to the model. That additional rigid structure represents again

3 the part of the hull shell in the collision zone, but now generated using coarse mesh elements. In another words, a hull shell in collision zone is modeled twice: once with the fine mesh elements are in contact with the striking ship and once with a coarse mesh elements that are in contact with the fluid. The two structures, naturally, overlap, since they represent the same structure. The reason for the generation of such overlapping structure will be explained later in the "Complete model" chapter. The overlapping coarse mesh structure is maintained lightweight so not to interfere with the total and correct mass of the ship. ambient ALE elements are able to behave as an infinite container of the fluid. Both the water and the air were defined by MAT_NULL LS-Dyna material model which is suitable for modeling the incompressible viscous laminar flow. This material requires an equation of state (EOS), defined by a polynomial, that is used for pressure evaluation (see Appendix for the EOS parameters used). Striking ship model Striking ship model is presented in Figure 2. The model is simplified in a way that, except the bow, ship is modeled using beam finite elements. The total mass of the beam elements plus the mass of the elements of the bow adds together in a total striking ship mass. Bow is modeled with a 3D finite element mesh consisting of elasticplastic plates and rigid bulkhead that connects the bow and the hull beam. Figure 3: Fluid model domains: 1 water, 2 air, 3 ambient air, 4 ambient water Complete model Figure 2: Striking ship model and bow detail The bow finite element mesh is rather coarse except at the bulb where fine finite element mesh is generated. However, bow structure is somewhat simplified internally since the deformation of the bow or the effect of bow in collision is not of the importance in this article. Complete model, with model parts at their position is presented in Figure 4. Please note that both the air and the ambient air domain are not presented in Figure 4. There are finite elements in total in a complete model. The analysis is set in a following manner. Striking ship has nothing to do with fluid domain. There is no contact or relation between the striking ship and the fluid domain of any kind. This is, of course, unrealistic but it simplifies the analysis model and reduces the calculation time significantly. On the other hand contact is defined between striking ship and a struck ship. Since the struck ship is rigid everywhere except in the fine mesh collision zone, contact between two ships is effectively the contact between a bow of the striking ship and a fine mesh zone of the struck ship. Fluid model Fluid model is a part of the analysis model that refers to the fluid environment and is presented in Figure 3. The model consists of four fluid domains; each of them modeled using multi-material solid ALE elements, where ALE stands for Arbitrary-Lagrangian-Eulerian formulation. Fluid domain 1 represents the water and it is generated using solid ALE finite elements having the equal edge lengths and volume of 1 m3. Fluid domain 2 represents the air and is modeled with the same size elements but having the properties of the air. Fluid domains 3 and 4 represent the ambient air and water, respectively. The Figure 4: Complete model (air and ambient air domain not presented) In this way, i.e. by neglecting the effect of the fluid on

4 the striking ship, but modeling the collision contact properly in every other way, the collision damage calculation is assumed to be realistic. Struck ship is immersed in the fluid completely. However, at the location of the overlapping hull shell a following condition is imposed. Fine mesh has no contact or relation with the fluid domain in any way and is used solely for the internal structural damage analysis, as already mentioned. On the other hand, overlapping rigid coarse mesh is immersed in the fluid but has nothing to do with structural damage. To summarize the things it can be said: striking ship will hit the struck ship in the fine mesh zone. During the collision, a striking ship, as well as the fine mesh in struck ship collision zone, will not be affected by fluid directly in any way. At the same time, struck ship shell, including the overlapping coarse mesh shell in the collision zone, is immersed in the fluid and is not affected by collision contact mechanics directly in any way. Only at the edges of the overlapping region the fine mesh shell and coarse mesh shell are connected by the merged nodes. In this way, striking ship kinetic energy is transformed into elastic and plastic deformation of the fine mesh collision zone, but, at the same time, through the merged nodes a part of its kinetic energy is also transformed into the global, collision induced motion of the struck ship model. To make things even more clear, following pictures illustrate the concept. Figure 5 presents a part of the model used for the "internal mechanics" analysis. Figure 6 presents a part of the model used for FSI analysis. The entire shell, including the overlapping shell segment in the collision zone is used for the "external dynamic" analysis. Figure 5: A part of the model used for damage analysis (fine mesh in the collision zone is clearly visible) FEM analysis By following the procedure of setting up the described FSI analysis method, the fluid domains were filled with water and air, respectively, the hull of the struck ship was discharged from the water below its water level line, the gravity was applied, while the usual hydrostatic pressure initialization was omitted for the sake of simplicity. Fixed boundary conditions were imposed to all the boundaries of the fluid domain so that fluid cannot go inside or outside of the domain. Striking ship model motion was constrained in z direction but no other constraints exist in the model. The struck ship floats freely through the balance of its own weight and induced buoyancy. The striking ship was given an initial speed and FSI calculation started. The FSI analysis of the complete model is a time consuming analysis and it takes approximately 50 hours of real time for the analysis of the 1 second of the model time on the reasonably powerful but otherwise regular desktop PC. Following figures illustrate the overall model behavior. The striking and struck ship contours are outlined only. The struck ship moves to the left, in global positive y- direction, and hits the struck ship starboard. Figure 7 presents the model at the beginning of the simulation. Struck ship cross-section is outlined completely, while the outline of the striking ship bow is visible on the right side. The presence of fluid is indicated by the red color LS-Dyna "iso surface", which is actually a boundary layer between fluids or fluid and structure. Figure 8 presents the model at t=0.3s of model time. The striking ship bow penetrated into a struck ship and generated significant damage. Up to this time striking ship kinetic energy is used almost entirely for the elastic and plastic deformation of the struck ship structure in the fine mesh zone. There is no visible motion of the liquid at this moment. Figure 9 presents the model at t=0.6 s. As the penetration and damage increased, the rolling motion of the struck ship, as well as the beginning of the violent sloshing of the surrounding water is initiated, as would be expected in reality. On Figure 10 the model is at t=0.9s. Collision process continues and surrounding water becomes more disturbed. In addition, the jaw motion of the struck ship becomes visible. Figure 11 presents the model at t=1.2s. Violent movement of the water, as well as jaw and roll of the struck ship are obvious. Finally, Figure 13 presents the model at t=1.2s seen from the top view. It should be noted that simulation is stable up to t=1.0s, and rather stable until t=1.6s when unrealistic rise of kinetic energy occurs. Figure 6: A part of the model used for FSI analysis

5 Discussion of the results Figure 7: Position at t=0 s Figure 8: Position at t=0.3 s Figure 9: Position at t=0.6s Discussion of the results will be following two paths: one related to stable simulation up to t=1.0s and the other related to the reasons for instabilities from that moment onwards. Setting up the FSI analysis is not a straightforward task. Once the user consults the LS-Dyna theoretical manual ( 2006), the LS-Dyna guidance manual ( 2010) and the related literature there still remain a number of open questions. Several major problems can be expected in FSI analysis using ALE method: leaking, problems with penalty forces and pressure, unstable calculation etc. Therefore, setting up the model should be carefully done. The first step is to correctly fill the domain with relevant fluids, which can be verified graphically by monitoring the fluid boundaries. Then, the Lagrangian domain should be properly related to the Eulerian domain i.e. the "inside" of the ship should be filled with air while the water should be "outside" of the ship hull. This again can be verified by looking at the boundary interface. Finally, gravity is applied. The hydrostatic pressure may be initialized but this was not done in the present analysis as most of the relevant effects occur on the water surface. However, hydrostatic pressure can be easily added at any moment. Within the first period, from t=0s to t=0.3s the fluid is virtually undisturbed as the striking ship and fluid relation is not existing and the deformation of the struck ship still does not transmit enough energy through the common i.e. merged nodes, to the rest of the (rigid) structure. This though happens from that moment on and the struck ship starts to roll and sway. Figure 12 presents the obtained contact force between two ships which has a maximum of 78.9MN at t=0.66s. This is in very good correlation with the previously made analysis where: if no hydrodynamic forces were present the peak contact force was 44.8 MN and when simplified hydrodynamic forces are present the peak contact force was 49.7 MN. This clearly shows that hydrodynamic drag forces, mainly due to sway, should be included in the analysis. Figure 10: Position at t=0.9s Figure 11: Position at t=1.2s Figure 12: Contact force vs. time, [N] vs. [s]

6 Proceedings of the ICCGS June, 2016 University of Ulsan, Ulsan, Korea Figure 13: Position at t=1.2s - view from above It is clear that even the simplified hydrodynamic forces affect the results significantly, yet still underestimating the effect of drag as shown by the present FSI analysis. Although the value of 78.9MN still needs to be carefully validated in the future research, the increase in the contact force clearly indicates the importance of fluid structure interaction. However, as mentioned earlier, the analysis from t=1.0s, and particularly from t=1.5s onwards, is not realistic. This can also be verified by looking at Figure 12. The contact force should decrease gradually since the striking ship pushes the struck ship as long as their kinetic energies become equal. Even more, it is often the case that two ships are stuck together when the event is over. On the Figure 12 the separation of two ships is clearly visible from approximately t=1.2s onwards. This occurs due to the excessive velocity in y-direction of the struck ship (and fluid) which is clearly a non-physical behavior. The reason for the error may be the incorrect coupling stiffness induced by sudden transfer of energy in impact. The coupling stiffness directly affects the coupling pressure and it is possible to control this by the user. However, this then requires a knowledge or estimation of the realistic coupling pressure vs. distance function that may be expected in the collision event. Also, a leaking problem was observed. Although that problem can sometimes be noticed by visual inspection of the simulation, LS-Dyna allows the information about leaking to be stored in a separate "DBFSI" database file. For example, it is clear from Figure 14 that significant amount of leakage occurred at t=0.58s. The induced forces may affect the results, but it seems this was not the case in the present analysis as contact forces seem uninterrupted by these additional. It is important to note that significant improvement of the simulation stability was achieved by simple smoothing of the struck ship shell: both the leaking was reduced and the stable calculation time was nearly doubled. In the physical sense, the leakage force is a coupling force resulting from the additional penetration prevention in penalty method. Normally, during the penetration of ALE element into the structure, coupling algorithm estimates the critical stiffness and applies compressive force to push that element out of the structure. If the penetration still occurs, an additional force is generated by coupling algorithm in order to prevent leakage and this represents the leakage force in LS- Dyna. Estimation of correct coupling stiffness is critical: too weak contact forces will not prevent leakage, while too strong contact forces may induce non-physical behavior of both structure and ALE elements. Conclusion Figure 14: Leakage forces An attempt to perform fully coupled FSI analysis using ALE method is presented. The analysis model consists of two ships colliding, of which the struck ship is immersed in the fluid. Presented analysis demonstrates the capability of a modern commercial software package, namely LS-

7 Dyna, to simulate the highly non-linear event in a complex environment. The performed analysis was partially successful. In the stable part of the analysis, collision was performed successfully. During the stable part kinetic energy was used for the internal damage mechanics resulting in a total contact force higher than the one obtained without and with simplified hydrodynamic effects taken into account. The increase of the contact force of 58.7% when compared to the simplified hydrodynamic collision analysis (78.9MN vs. 49.7MN) indicate that drag due to sway and roll motion of the struck ship presents the important part of the analysis, significantly affecting the result i.e. the amount of the damage. On the other hand, in the unstable part of the analysis the kinetic energy of the system rises without any physical reasons to the unacceptable levels. The reason for that is either and error in the model set-up or the limits of the software in capturing the phenomena involved in FSI collision analysis such as violent fluid motion and high contact pressure induced. It may be concluded that LS-Dyna, as well as any other equally capable software, can be a powerful tool in the hands of the skilled user. However, mastering the software with limited information on its functionality is a well-known problem. In the light of that fact the authors will continue to examine the possible sources of the problems in the present analysis model. Acknowledgment: This work has been supported in part by Croatian Science Foundation under the project References for_mgd_18oct2010.pdf s/ls-dyna_theory_manual_2006.pdf Gagnon R. E., Wang J Comprehensive Numerical Simulations of a Tanker Collision with a Bergy Bit Incorporating Damage to the Vessel, 21st International Symposium on Ice, Dalian, China, p Lee, S.G., Zhao, T. and Nam, J.H Structural safety assessment of ship collision and grounding using FSI analysis technique, Proceedings of the 6th International conference "Collision and Grounding of Ships and Offshore Structures", ICCGS 2013, Trondheim, Norway, p Ozguc O., Das P. K., Barltrop N A comparative study on the structural integrity of single and double side skin bulk carriers under collision damage, Marine Structures 18 (2005) pp Pedersen P. T Review and application of ship collision and grounding analysis procedures, Marine Structures 23 (2010) pp Rudan S., Tabri K., Klarić I Analysis of sloshing interaction in ship collisions by means of ALE finite element method, Proceedings of 5th International Conference on Collision and Grounding of Ships, Espoo, Finland, p Rudan S., Aščić B., Višić I Crashworthiness study of LPG ship with type C tanks, Proceedings of 6th International Conference on Collision and Grounding of Ships and Offshore Structures, ICCGS 2013, Trondheim, Norway, p Rudan S., Aščić B Crashworthiness of type C tanks in LPG ship, Proceedings of 33rd International Conference on Ocean, Offshore and Arctic Engineering OMAE 2014, San Francisco, California, USA, paper OMAE Tabri K., Broekhuijsen J, Matusiak J, Varsta P Analytical modelling of ship collision based on fullscale experiments, Marine Structures 22 (2009) pp Zhang A., Suzuki k A comparative study of numerical simulations for fluid structure interaction of liquid-filled tank during ship collision, Ocean Engineering 34 (2007) pp Appendix LS-Dyna ALE properties used in the article: Water Air *MAT_NULL mid, ro, pc, mu, terod, cerod, ym, pr 5, , , 1.0E-3, 0.0, 0.0, 0.0, 0.0 *EOS_GRUNEISEN eosid, c, s1, s2, s3, gamao, a, e0, v0 1, , 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 *MAT_NULL mid, ro, pc, mu, terod, cerod, ym, pr 16, , -10.0, 1.85E-5, 0.0, 0.0, 0.0, 0.0 *EOS_GRUNEISEN eosid, c0, c1, c2, c3, c4, c5, c6, e0, v0 3, 0.0, 0.0, 0.0, 0.0, 0.4, 0.4, 0.0, e+5, 1.0