Direct simulation of zigzag maneuver for fully appended ship

Direct simulation of zigzag maneuver for fully appended ship Jianhua Wang, Decheng Wan * 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 * Email: dcwan@sjtu.edu.cn ABSTRACT In this paper, a CFD-based method coupling with overset grid technique is used to directly simulate the 20/20 zigzag maneuver of the fully appended ONR Tumblehome ship model. Numerical computations are carried out by our in-house CFD code naoe-foam-sjtu, which is developed on the open source platform OpenFOAM. The overset grid module is used to predict the ship motions with 20/20 zigzag maneuver. The ship model is advancing at its model point obtained by our CFD results in calm water. Detailed information of the flow field during the zigzag maneuver is presented and analyzed. In addition, predicted results, i.e. ship motions, rudder angle and yaw rate are also presented and compared with the available experimental data. Good agreements are achieved which indicate that the present approach is applicable for the direct simulation of zigzag maneuver for fully appended ship. KEY WORDS: Overset grid; zigzag maneuver; naoe-foam-sjtu solver; OpenFOAM INTRODUCTION Growing capability of Computational Fluid Dynamics (CFD) has opened new horizons in the research field of ship hydrodynamics, including seakeeping, propulsion, and maneuvering. However great challenges still remain in the area of ship hydrodynamics, and direct computations of ship maneuvering problems are especially difficult, mostly due to limitations of traditional meshing methodologies to handle moving geometries. The dynamic overset grid technology opens the possibility of computation of complex motions, including self-propulsion with moving rudders and rotating propellers and zigzag or turning circle maneuver. Recently, dynamic overset grid method has been successfully applied to study the hydrodynamic performance in directly simulating hullpropeller-rudder interaction. Carrica et al. (2012) [1] uses URANS approach coupled with dynamic overset grids to study the turn and zigzag maneuvers of a surface combatant. And in his study, the propeller is simplified as an actuator disk/ body-force in which local velocity effects on the propellers are neglected. Numerical results are mostly within 10% compared to the experimental data. Broglia et al. (2015) [2] takes the same approach to study the turning maneuver of a fully appended twin screw vessel using a finite volume method CFD solver. Further analysis for the distribution of forces and moments on the hull, appendages and rudders has been done to gain the dynamic behavior in turning tests. Shen et al. (2015) [3] implements dynamic overset grid module to OpenFOAM and applied to the KCS self-propulsion and zigzag maneuvering simulation. Direct simulation of hull, propeller and rudder interaction is applied and the numerical results show that the overset grid method is applicable for the computations of ship hull, propeller and rudder interaction. Carrica et al. (2016) [4] reported the direct simulation of zigzag maneuver for KCS in shallow water. Full discretized propeller model is used in this condition and grid uncertainty studies are also conducted with grids up to 71.3 million points. Direct simulated results show satisfactory agreements with the experimental results for most of the variables. In this paper, numerical simulations are performed to study the hydrodynamic performance of fully appended ONR Tumblehome ship model with 20/20 zigzag maneuver. All the numerical computations are carried out by our in-house CFD solver naoe-foam-sjtu. Detailed information of the flow field during the zigzag maneuver is presented and analyzed. In addition, predicted results, i.e. ship motions and rudder angle, yaw rate are also presented and compared with the available experimental data. Good agreements are achieved which indicate that

the present approach is applicable for the direct simulation of zigzag maneuver for fully appended ship. NUMERICAL APPROACH naoe-foam-sjtu Solver The in-house CFD solver naoe-foam-sjtu solves the Navier-Stokes equations for unsteady turbulent flows with VOF method capturing free surface around the complex geometry models. The framework of naoe-foam- SJTU solver and its main features are only briefly presented here: the solver is developed on the open source platform OpenFOAM and has the ability of handling complex 6DoF motions with a hierarchy of bodies through overset grid method. More details of naoe-foam-sjtu solver can be referred to Shen et al. (2014, 2015, 2016) [3,5,6], Cao et al. (2014, 2015) [7,8], Zha et al. (2015) [9] and Wang et al. (2015a, 2015b) [10,11]. The URANS equations and VOF transport equation are discretized by the finite volume method (FVM), and the merged PISO-SIMPLE (PIMPLE) algorithm is applied to solve the coupled equations for velocity and pressure field. Near wall treatment wall functions are applied to the moving wall boundary, which can reduce computational grid with coarse layer near the ship ( can be more than 30). In addition, several built-in numerical schemes in OpenFOAM are used in solving the partial differential equations (PDE). y Overset Grid Technique The overset grid module is the key point for direct simulating the fully coupled hull, propeller and rudder system. Overset grid comprises of two or more blocks of overlapping structured or unstructured grids. By using dynamic overset grid techniques, the overlapping grids can move independently without constraints. To achieve this, the cells in the computational domain are classified into several types, i.e. fringe, hole, donor etc. The information of these is contained in the domain connectivity information (DCI) file. In our present solver, Suggar++ (Noack et al., 2009) [12] is utilized to generate the domain connectivity information (DCI) for the overset grid interpolation. With the dynamic overset grid capability, the full 6DoF motion solver allows the ship hull as well as the rotating propellers and moving rudders to move simultaneously. Two coordinate systems are used to solve the 6DoF equations. One is the inertial system (earth-fixed system) and the other is non-inertial system (ship-fixed system). The inertial system can be fixed to earth or move at a constant speed with respect to the ship (here we only apply the horizontal motion for the moving of inertial system). The non-inertial system is fixed to the ship and can translate or rotate according to the ship motions. Details of the 6DoF module with overset grid module implementation can be found in Shen et al., (2015) [3]. In our present study, the complex geometry is decomposed into several overlapping grids, and can be used to handle complex motion problems, especially for the numerical simulation of zigzag maneuver. GEOMETRY, GRID AND TEST CONDITIONS Geometry model The ship model in the present simulations is the ONR Tumblehome model 5613, which is a preliminary design of a modern surface combatant fully appended with skeg and bilge keels. The model also has rudders, shafts and propellers with propeller shaft brackets. The geometry of ONR Tumblehome is shown in Fig. 1, and the principle geometric characteristics are listed in Table 1. Fig. 1 Geometry model of ONR Tumblehome Table 1 Principle dimensions of fully appended ship Main particulars Model scale Full scale Length of waterline LWL ( m ) 3.147 154.0 Beam of waterline BWL ( m ) 0.384 18.78 Draft T ( m ) 0.112 5.494

Displacement Propeller diameter Propeller shaft angle DP ( kg) ( m) 72.6 8.507e6 0.1066 NA (deg.) 5 NA Propeller rotation inward inward Rudder rate 35.0 deg./s Grid Distribution To directly simulate the standard 20/20 zigzag maneuver, the computational domain is divided into six parts: one for the background grid, one for grid around ship hull, two for the grids around propeller in starboard side and port side, two parts for both side rudders. Six part grids have overlapping areas and the grid arrangement is shown in Fig. 2. The local grid distribution around ship hull, propeller and rudder is shown in Fig. 3 and the total grid number for the simulation is 6.81M. Fig. 2 Overset grid arrangement Fig. 3 Local grid distribution around propeller and rudder Test Conditions The fully appended ship is set to advance at model point in calm water with rotating propellers and moving rudders The approaching speed is U0 1.11 m/s ( Fr 0.20 ). Standard 20/20 zigzag maneuver test is carried out for the present numerical simulation. During the procedure, the rate of resolution RPS is set to 8.81 according to our previous CFD results for self-propulsion simulation and the calculation is restarted from the final steady state of the self-propulsion. SIMULATION RESULTS The zigzag maneuver is started from the self-propulsion condition, letting the ship free in full 6DoF and executing the rudder according to the zigzag maneuver. During the simulation, the propeller rotational speed is maintained constant at the self-propulsion model point. The time step is set to 0.0004s considering the high speed for the rotating propeller. Simulation time for model scale is 31s and the rudder has been executed for 4 times. In addition, the zigzag maneuver has completed a cycle. Fig. 4 shows the time histories of rudder angle and yaw motion of the 20/20 zigzag simulation and the results are also compared with the experimental result (Elshiekh, 2014) [13]. The comparison in terms of the rudder angle and the yaw motion shows an overall agreement between the numerical result and the experimental data. Table 4 lists the comparison of 20/20 zigzag test parameters. Table 2 Parameters for the 20/20 zigzag maneuver Parameters EFD CFD First overshoot (deg) 5.92 5.02 Second overshoot (deg) 5.49 3.99 Third overshoot (deg) 5.50 5.01 Period 15.81s 15.68s First execute 2.41s 2.52s Third execute 15.38s 15.74s

From Table 2 we can see that the predicted results for the overshoot angles are underestimated compared to the experimental results with the largest error of 27% (second overshoot angle). As for the period to complete a cycle, the simulation result is 15.68s, very close to the experimental period 15.81s. Finally Table 2 shows the time for the first execute and third execute. Variations in initial conditions for yaw and yaw rates cause differences in the time for the first execute with errors up to 4.56%. By the time the third execute is reached the differences have been overcome by the transients of the maneuver and the error is decreased to 2.34%. Fig. 4 Time histories of rudder angle and yaw motion Fig. 5 Time histories of roll motion Fig. 6 Time histories of yaw rate Fig. 5 shows the time histories of roll motion of the 20/20 zigzag maneuver. The results are very close to the experimental, though the maximum roll angle is slightly under predicted. Fig. 6 shows the yaw rate comparison between the predicted results and the experimental data. The numerical result is under predicted compared to the available measurements. Above all, the numerical results of the 20/20 standard zigzag test show an overall agreement with the test data and confirm that the predicted results are reliable. Fig. 7 presents the wave patterns in one zigzag simulation period. Four snapshots at zero, maximum and minimum yaw angle are chosen to analyze the flow field during the zigzag test. After the rudder first execute to the port side, the ship hull is under a positive lateral force excited by the rudder. Due to the lateral force, the yaw motion of the ship model then increases. After the yaw angle comes to 20, the rudder starts execute to the starboard side with an increasing negative lateral force. The yaw angle continues to increase and the maximum value is the first overshoot angle (shown in Fig. 7a). Fig. 7c shows the wave patterns at second overshoot angle. The wave patterns experience significant changes due to the ship motion, especially with the largest yaw motion. Fig. 8 describes the vortical structures displayed as isosurfaces of Q=200 colored by axial velocity. Strong interaction is observed between the ship hull, propellers and rudders. Furthermore, the rudder can strongly affect the vortex of propeller. In Fig. 8a, where comes with the first overshoot angle, the hub vortex of leeward propeller is rarely small compared to the windward propeller. The phenomenon is opposite in Fig. 8c, where comes with the second overshoot angle. When it comes to the zero yaw angle, the path of the hub vortex shows significantly

difference with its direction due to the turning rate. The detailed flow information can explain the hydrodynamic characteristics of the standard 20/20 zigzag maneuver. a) max b) 0 c) min d) Fig. 7 Wave patterns at zero, maximum and minimum yaw angle 0 a) max b) 0 c) min d) 0 Fig. 8 Iso-surfaces Q colored by axial velocity at zero, maximum and minimum yaw angle CONCLUSIONS

This paper presents the standard 20/20 zigzag maneuver simulation of fully appended ONR Tumblehome ship model. Computations are carried out using our in-house CFD solver naoe-foam-sjtu. During the process, the moving rudders and rotating propellers are handled by the dynamic overset grid method. A specified zigzag maneuver rudder is used to achieve the desired ship motion. The numerical results of rudder angle, yaw motion, roll motion and yaw rate are presented and compared to the experiment. Good agreement is observed for the zigzag period with error of 0.82%. Other key parameters, such as overshoot angle, rudder execute time, are also in accordance with the experimental data. Furthermore, the wave patterns and vortical structures are presented at zero, maximum and minimum yaw angle to illustrate the hydrodynamic characteristics of standard 20/20 zigzag maneuver. High accuracy of the predicted results confirm that the present CFD method coupled with dynamic overset gird technology is applicable for the prediction of zigzag maneuver. ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (51379125, 51490675, 11432009, 51579145, 11272120), Chang Jiang Scholars Program (T2014099), 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), to which the authors are most grateful. REFERENCES [1] CARRICA P M, ISMAIL F, HYMAN M, et al. Turn and zigzag maneuvers of a surface combatant using a URANS approach with dynamic overset grids[j]. Journal of Marine Science and Technology, 2012, 18(2): 166 181. [2] BROGLIA R, DUBBIOSO G, DURANTE D, et al. Turning ability analysis of a fully appended twin screw vessel by CFD. Part I: Single rudder configuration[j]. Ocean Engineering, 2015, 105: 275 286. [3] SHEN Z, WAN D, CARRICA P M. Dynamic overset grids in OpenFOAM with application to KCS self-propulsion and maneuvering[j]. Ocean Engineering, 2015, 108: 287 306. [4] CARRICA P M, MOFIDI A, ELOOT K, et al. Direct simulation and experimental study of zigzag maneuver of KCS in shallow water[j]. Ocean Engineering, 2016, 112: 117 133. [5] SHEN Z, ZHAO W, WANG J, et al. Manual of CFD solver for ship and ocean engineering flows: naoe-foam- SJTU[J]. 2014: Shanghai Jiao Tong University. [6] SHEN Z, WAN D. An irregular wave generating approach based on naoe-foam-sjtu solver[j]. China Ocean Engineering, 2016, 30: 177 192. [7] CAO H, WAN D. Development of Multidirectional Nonlinear Numerical Wave Tank by naoe-foam-sjtu Solver[J]. International Journal of Ocean System Engineering, 2014, 4(1): 52 59. [8] CAO H, WAN D. RANS-VOF solver for solitary wave run-up on a circular cylinder[j]. China Ocean Engineering, 2015, 29: 183 196. [9] ZHA R, YE H, SHEN Z, et al. Numerical computations of resistance of high speed catamaran in calm water[j]. Journal of Hydrodynamics, Ser. B, 2015, 26(6): 930 938. [10] WANG J, LIU X, WAN D. Numerical Simulation of an Oblique Towed Ship by naoe-foam-sjtu Solver[C] Proceedings of 25th International Offshore and Polar Engineering Conference. Big Island, Hawaii, USA: 2015. [11] WANG J, LIU X, WAN D. Numerical prediction of free runing at model point for ONR Tumblehome using overset grid method[c] Proceedings of CFD Workshop 2015. Tokyo, Japan: 2015, 3: 383 388. [12] NOACK R W, BOGER D A, KUNZ R F, et al. Suggar++: An improved general overset grid assembly capability[c] Proceedings of the 47th AIAA Aerospace Science and Exhibit. San Antonio TX: 2009: 22 25. [13] ELSHIEKH H. Maneuvering characteristics in calm water and regular waves for ONR Tumblehome[D]. The University of IOWA, 2014.