SHIP MOTIONS OF KCS IN HEAD WAVES WITH ROTATING PROPELLER USING OVERSET GRID METHOD

Transcription

1 Proceedings of the ASME rd nternational Conference on Ocean, Offshore and Arctic Engineering OMAE2014 June 8-13, 2014, San Francisco, California, USA OMAE SHP MOTONS OF KCS N HEAD WAVES WTH ROTATNG PROPELLER USNG OVERSET GRD METHOD Pablo M. Carrica HR-Hydroscience and Engineering, The University of owa owa City, owa, USA Zhirong Shen School of Naval Architecture, Ocean and Civil Engineering, State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University Shanghai, China Decheng Wan* School of Naval Architecture, Ocean and Civil Engineering, State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University Shanghai, China experiments, potential theories, and computational fluid dynamics (CFD). Among them, CFD has gained popularity in the past decade due to a more physics-based modeling, capability of handling non-linear free-surface, especially for largeamplitude waves and induced violent ship motions and breaking waves. CFD is also becoming more mature and robust with the development of better computational techniques and numerical schemes. Many achievements have been made to investigate the seakeeping problems using CFD approaches in the past decade. Carrica, et al. [1] simulated the seakeeping of DTMB12 in head waves using overset grids method. The computation of two ships heaving and pitching one behind the other was performed to demonstrate the overset grids. Shen, et al. [2] performed the same DTMB12 model in head waves to investigate the motion responses and added resistances by OpenFOAM using dynamic deforming mesh approach. Both EFD and CFD investigations for the KCS model in head waves were performed by Simonsen, et al. [3]. A fully CFD verification and validation of seakeeping for KVLCC2 in head waves were studied by Sadat-Hosseini et al. [4]. The study was conducted for both short and long waves and free and fixed surge conditions. However, for self-propulsion in waves, almost all CFD studies of seakeeping only investigate the bare hull and ignore the effects of the propellers due to the complexity of the problem. ABSTRACT The overset grid method has been implemented in the open source code OpenFOAM. The purpose of this work is to validate the overset code in OpenFOAM and demonstrate the capability and flexibility of overset grid approach to solve complex situations. Ship motions of KCS in head waves with and without rotating propeller are investigated using overset grid method in this paper. Two conditions are conducted. The first case involves the model without propeller advancing at a speed of m/s, corresponding to Fr=0.26 and Re= ncident regular wave of wave length =1.1Lpp and wave height Hw=0.084m is adopted. A grid convergence study is conducted for the validation of overset grid method. n the second case, a rotating propeller is installed on the KCS model. The seakeeping characteristics of KCS model with rotating propeller in head waves are investigated numerically. The motion responses and propeller thrust and torque are analyzed and compared with experimental data. 1 NTRODUCTON Seakeeping is one of the most important topics in ship hydrodynamics because it is related to powering characteristics and safety of crew and ship. There are several ways to predict ship motions and added resistance in waves, including * Corresponding author. dcwan@sjtu.edu.cn 1 Copyright 2014 by ASME

2 Self-propulsion in waves combines the motion of the ship in waves and rotation of propeller and it is a great challenge for conventional moving mesh techniques to handle these two motions simultaneously. Dynamic overset grids provide an effective way to overcome these problems. t allows large-amplitude 6DOF motions of ships in waves and includes a hierarchy of objects, which makes it possible for appendages such as propeller, rudder, etc. to move independently with respect to the motions of the ship. The work handling both ship motions in waves and rotating propeller is limited. Carrica, et al. [] simulated broaching events of a fully appended ONR tumblehome model DTMB 613 with moving rudders and rotating propellers in following regular waves. n this paper, the computations are performed with the RANS solver naoefoam-os-sjtu with dynamic overset grid capability. This solver is an upgrade version of the previous solver naoefoam-sjtu [2] and it is developed based on the open source CFD code OpenFOAM. The domain connectivity information (DC) is generated by the Suggar library [6] to build the connection between the overset component grids. A full 6DOF module with a body hierarchy enabling moving appendages is implemented. This solver is implemented with a wave generation system, which is able to generate different wave types, including regular and irregular waves and short- and longcrest waves with a variety of spectra. 2 COMPUTATONAL METHODS The governing equations are the incompressible Reynolds- Averaged Navier-Stokes (RANS) equations. The Volume of fluid (VOF) method with an artificial compression technique is applied to capture the two-phase interface. The coupled velocity and pressure are solved by PSO algorithm. The k-ω Shear- Stress transport (SST) model [7] is chosen for the turbulence closure. All these methodologies are provided by the original OpenFOAM library. For details refer to [8,9]. The overset grid technique is implemented into OpenFOAM to handle the large-amplitude motion of ship and complex hierarchical motion of appendages such as rotating propeller and moving rudder. The overset grid method allows separate overlapping grids to move independently without restrictions. The overset approach implemented in this work requires domain connectivity information (DC) to build the communication among separate overset grids. The Suggar library [6] is called to generated the DC for OpenFOAM. A lagged mode as described in [10] is applied to allow OpenFOAM and Suggar to perform computations simultaneously to avoid unnecessary waiting time. A fully 6DOF module with hierarchy of bodies are implemented. This module allows ship to move independently in the computational domain and in the meanwhile, the propeller is rotating around the propeller axis. Two coordinate system, earth-fixed and ship-fixed systems, are adopted in this 6DOF module. The forces and moments on ship hull and propeller are computed in earth-fixed system and then they are projected to ship-fixed system. The ship motions for the next time step are predicted by the projected forces and moments in ship fixed system. For the movements of hierarchal objects, the propeller grid rotates first about a fixed axis in the ship coordinate system, and then both ship and propeller grids translate and rotate in the earth-fixed system according to the predicted motions. n the meanwhile, Suggar library is called to compute the DC based on the new grid positions. OpenFOAM processors receive the new data right after the movements of the overset grids and start the computation for the next time step. For the details of the implementations of overset capability and 6DOF module can be referred to [11]. The incoming regular wave is generated by imposing the boundary conditions of and U at the inlet. The linear Stokes wave in deep water is applied for the wave generation. ( x, t) acosk xxcg et (1) uxyzt (,,, ) U kz 0 ae cosk xxcg et (2) wxyzt (,,, ) ae kz sink xxcg et where is the wave elevation; a is the wave amplitude; k is the wave number; U 0 is the ship velocity; is the natural frequency of wave; e is the encounter frequency, given by e = e + ku 0 in head waves; x cg is the longitudinal gravity center of the ship model. x cg is used to adjust the phase of the incident wave to make the wave crest reach the gravity center of ship at t = 0. 3 GEOMETRY AND CONDTONS KCS is a modern container ship developed by the Korean Maritime and ocean Engineering Research nstitute (MOER, formerly KRSO). The model was conceived to provide data for CFD validation in the past decade. The ship model used in this work is HSVA KCS model with scale factor of = The geometry of the HSVA KCS model is illustrated in Figure 1 and detailed particulars of the HSVA KCS model are listed in Table 1. The HSVA KCS model is equipped with a rudder and a fiveblade propeller (SVP 1193). The main particulars of the propeller are listed in Table 2. The ship model is free to heave and pitch at a service speed of m/s, corresponding to Fr=0.26 and Re= The experiments were performed in FORCE Technology s deep water towing tank in Lyngby, Denmark [12]. Figure 1 Geometry of HSVA KCS model with propeller and rudder appended (3) 2 Copyright 2014 by ASME

3 Table 1: Geometrical properties of KCS model Model Main particulars Symbol scale Scale factor Length between perpendiculars Lpp (m) (m) Length of waterline Lwl Beam of waterline Bwl (m) Draft T (m) Displacement (m3 ) Wetted area without rudder Sw (m ) Block coefficient CB (m) 0.60 Longitudinal center of gravity LCG (m) (from midship, fwd+) Vertical center of gravity (from VCG(m) waterline) Moment of inertia Kyy/Lpp 0.2 Full Scale Figure 2 Layout the of computational domain KCS without propeller & Grid convergence test n order to validate the overset approach applied to the investigation seakeeping problems, a grid convergence study of the KCS hull appended with rudder is carried out first. Due to the large expense of modelling the propeller for the finest grid, the KCS model appended with propeller has not been included in the grid convergence study. 0.2 Table 2: Main particulars of SVP-1193 propeller (model scale) Main particulars Symbol Value Diameter D (mm) 10.0 Pitch ratio at 0.7 P0.7/D Area ratio Ae/Ao Hub ratio dh/d Number of blades Z Direction of rotation Right-handed The wave condition of Hw =0.084 m in the experiment is chosen for the computation. The wave period is T=1.78 s coresponding to Hw 1/60. The ship speed is U0=1.701 m/s, resulting in the encoutner frequency fe=0.91 Hz. This wave condition is chosen to investiage the large-amplitude motions and non-linear forces and moments near resonance condition. The natual wave frequency is estimated to be fe 0.9 Hz [3], resulting in fe fn at the service speed. The wave lengthl /Lpp=1.1 is close to /Lpp = 1.33, in which the ship may have maximum motion response according to [13]. The details of the wave condition is summarized in Table 3. The layout of the compuational domain is shown in Figure 2. One wave height probe is set at Lpp/2 away in the transversal direction but at the same position as the ship bow in the longitudinal direction to measure the wave elevation. Hw (m) Table 3 Wave condition T (s) U0 (m/s) Te (s) /Lpp RESULTS AND DSCUSSONS Figure 3 Overset grids for KCS model (Medium grid) Table 4 Details of grid size for grid convergence test Grid Size Hull Background Total Coarse Medium Fine fe (Hz) , ,348 29,91 7,480 1,41,277 91,148 2,9,96 1,08,628 4,101, 233 Figure 3 illustrates the overset grids for the KCS model. The overset grids consist of hull and background grids. The hull grid, which resolves the near hull flows, moves with the ship model and the background grid is fixed in the earth-fixed coordinate system. The grids are generated by SnappyHexMesh, an automatic mesh generation tool provided by OpenFOAM. This 3 Copyright 2014 by ASME

4 tool generates mesh based on Cartesian grids by splitting hexahedral cells, resulting in unstructured octree-hexahedral grids. Only half the computational domain is generated due to the symmetry of the problems. The grid refinement procedure is to refine the Cartesian grids first with specified refinement ratio and then run SnappyHexMesh. This procedure can produce approximately consistent refined meshes for unstructured meshes. The refinement ratio in this study is 2 for three directions and the details of grid sizes are listed in Table 4. Figure 3 represents the medium grid in this table. The time histories of wave heights for three grids measured by the wave probe are shown in Figure 4. The amplitudes of incoming wave are obtained through Fourier Series expansion, as listed in Table. There is no noticeable difference among the three grids observed from the time histories. The target amplitude of incident is =0.042 m and all measured amplitudes for three grids are close to the target. Even for the coarsest mesh, the error is less than 0.%. Figures and 6 show time histories of heave and pitch motions for three grids respectively. Similar with the results of wave elevation, the predicted motions with different grids are almost identical even if the grid size of finest grid is 8 times larger than the size of the coarsest one. summaries the transfer functions TF 3 and TF of heave and pitch responses respectively, compared with experimental data. The transfer functions are defined as: x3 1 TF3 (4) x 1 TF k in which x 3 1 and x 1 are the 1st harmonic amplitude of heave and pitch motions respectively; is the amplitude of the linear incident wave. Both the results of TF 3 and TF converge. TF 3 presents oscillatory convergence and TF indicates monotonic convergence. The results of finest grid are compared with measurements, resulting in the errors of -4.01% for TF 3 and -0.39% for TF. Figure 4 Time histories of surface elevation measured by wave probe with different grids Figure Time histories of heave motion for different grids Figure 6 Time histories of pitch motion for different grids Table Wave amplitude measured by wave probe Coarse Medium Fine Target (m) Table 6 Results of transfer function of heave and pitch motions (The errors are compared by Fine grid and EFD) Coarse Medium Fine EFD Error (%) TF % TF % Figure 7 illustrates the time histories of resistance coefficients C t for different grids. C t is defined as: X Ct () 2 0.SwU0 where X is the integral force acted on ship hull in x direction of earth-fixed coordinate system, is the density of water and S w is the static wetted area of the hull. Unlike the heave and pitch motions, discrepancies can be observed for the resistance among different grids and the time histories of resistance indicate strong non-linearity. Table 7 lists the results of added resistance with different grids. The added resistance aw is defined as ( X 0 X calm ) aw (6) 2 2 g B / LPP where X 0 is the mean value of X; X calm is the steady-state resitance in calm water. X calm = N is obtained in the calm water computation using the medium grid. The resistance shows more sensitive to grid density than heave and pitch motions do. The difference of relative errors between coarse and medium grids is 4.9%. The results of aw achieve oscillatory convergence. The smallest error is obtained by medium grid and finest grid has a 0.9% larger error. This is most likely due to the fact that all aw 4 Copyright 2014 by ASME

5 of wave height in the experiment. The averaged decay of wave height for this wave condition (H=0.084 m) was estimated as m according to the experiment report, contributing to the uncentainties of measured heave and pitch motions. Compared with the results with no propeller listed in Table 6, the predicted TF3 and TF of self-propulsion are reduced by 2.2% and 1.8% respectively. are calculated by the Xcalm using the medium grid. The error for the fine grid may be reduced if Xcalm is obtained by the finest grid. Overall, the grid convergence study shows good convergnce for motions and forces and good quantitive results compared with experiments. Table 8 Grid sizes of overset component grids Hull Propeller Background Total Grid Size 2,931,764 78,989 1,098,416 4,789,169 Figure 7 Time histories of resistance coefficients by different grids X 0 (N) aw (-) Error (%) 4.2 Table 7 Results of added resistance Coarse Medium Fine EFD Self-propulsion The self-propulsion is performed in the same wave condition as in the grid convergence study but with propeller appended on the KCS model. Figure 8 illustrates the overset grids for the HSVA KCS model with propeller. The summary of overset component grids is listed in Table 8. The computational grids are similar to the medium grid in the grid convergence study but have an additional propeller grid, refinement regions designed to capture propeller vortices and full geometry without symmetry boundary condition. All grids are generated by SnappyHexMesh resulting in around 4.8 M total grid cells. The computation time for this case is in total 9300 CPU hours by 96 processors with the duration of 1 encounter wave periods. Among all of the CPU processors, 92 are running OpenFOAM and the rest are running Suggar. The propeller speed is set to be revolutions per second (RPS), which is determined by a self-propulsion test in calm water. During the self-propulsion test, the propeller speed is adjusted continuously by a P controller until the target ship speed and the equilibrium of resistance and thrust are achieved. The predicted RPS is 1.84% higher than the experimental value (14.1 RPS). The time histories of heave and pitch motions compared with measurements are shown in Figure 9. The predicted motions closely agree with EFD but the ship responses slightly earlier than EFD. The predicted transfer functions TF3 and TF obtained by Fourier Series expansion are listed in Table 9. TF3 is slightly under-predicted by -0.71% while TF has overprediction of 7.12%. The error of TF might be due to the decay Figure 8 Overset grid of HSVA KCS model with propeller (a) Heave motion (b) Pitch motion Figure 9 Time history of ship motions Copyright 2014 by ASME

6 Table 9 Transfer functions of heave and pitch for self-propelled KCS in head wave CFD EFD Error (%) TF TF Figure 10 presents the comparisons of time histories for propeller thrust. The computational result shows a similar trend as EFD but CFD presents a more sinusoidal curve than EFD, which is consistent to the periodic motions of ship in the head wave. The higher frequency oscillation is captured by CFD, which is five times the speed of the propeller rotation speed. (14.41 RPS). When each of the five propeller blades passes through the non-uniform wake flow at propeller plane, it causes an oscillation of propeller load. EFD wasn t able to capture the higher frequency oscillation due to the lower sampling frequency, which was 4 Hz reported by the experiment. The time histories of propeller torque show similar curves as propeller thrust but the comparison between EFD and CFD shows relatively larger discrepancy. The predicted torque presents a similar sinusoidal curve as the thrust does while no periodic behavior is observed from the EFD data for the torque. The reason for the discrepancy might be the insufficient accuracy of torque measurement in the experiment. More work will be emphasized to investigate the discrepancy in future work. Table 10 lists the comparisons of averaged propeller thrust and torque. The predicted mean thrust and torque are underpredicted by 2.29% and 4.42% compared with measurements. Figure 10 Time history of propeller thrust Figure 11 Time histories of propeller torque Table 10 Mean values of propeller thrust and torque n (RPS) T Mean (N) Q Mean(Nm) EFD CFD (1.84%) (-2.29%) (-4.42%) Figure 12 illustrates the four snapshots of free surface and ship motion during one encounter period. At t/t e =0, the wave trough comes to the ship bow. Nearly all the ship bow except the bulbous bow comes out of the water. The overturn of the bow wave is observed at t/t e=0.2. At t/t e=0., the wave crest reaches the ship bow that is nearly buried into water. At t/t e =0.7, the wave crest is pass through the ship bow and the bow is turning up and turning to the position at t/t e=0. Four snapshots of the iso-surfaces of Q=100, the second invariant of the velocity gradient tensor, to illustrate the propeller vortices after ship stern are shown in Figure 13. The iso-surfaces are colored by the velocity magnitude. The propeller tip, root and hub vortices interacted with the rudder can be clearly observed. The velocity of propeller vortices at t/t e =0 and 0.2 is lower than t/t e =0. and 0.7. At t/t e =0 and 0.2, the ship stern is in the region of wave trough. The wave velocity is in the opposite direction of ship speed. The absolute velocity at propeller plane is reduced, contributing to the increase of propeller load. At t/t e =0. and 0.7, on the contrary, the ship stern is close to wave crest and positive wave velocity increases the wake velocity and reduces the load on propeller blades. The changes of propeller loads can also be proven by the time histories of propeller thrust and torque shown in Figures 10 and Copyright 2014 by ASME

7 (a) t/te = 0 (a) t/te = 0 (b) t/te =0.2 (b) t/te =0.2 (c) t/te =0. (c) t/te =0.0 (d) t/te =0. Figure 12 Snapshots of free surface and ship motion in one period (d) t/te =0.7 Figure 13 Snapshots of Q iso-surfaces in one period 7 Copyright 2014 by ASME

8 CONCLUSONS n this paper, the computations of KCS without and with rotating propeller in head wave were presented. The aim of this work is to validate the overset grid method implemented in the OpenFOAM code and to demonstrate the great flexibility and capability and of overset approach when handling complex situations. A grid convergence study was performed first to validate the overset approach with 6DOF module and wave generation system. The predicted motion responses and added resistance indicated good convergence. The comparison between the finest grid and experiment showed good agreement. The simulation of KCS model with rotating propeller in the same wave condition was performed after the grid convergence study. Good agreements between CFD and EFD were achieved for the ship motions as well as the mean propeller thrust and torque. The propeller vortices interacted with rudder at different stage of the regular wave was clearly observed. The results of this work validate the overset code in OpenFOAM and show the high accuracy and flexibility of predictions of ship motions and forces in head waves. Of most importance, it proves the capability of OpenFOAM for handling the complex situations such as ship heaving and pitching in waves appended with rotating propeller. For the future work, a systematic grid and time convergence study will be performed for the seakeeping of KCS with rotating propeller to validate further the overset code based on OpenFOAM. More wave conditions will be generated to investigate deeply the effects of propeller on ship forces and motions. ACKNOWLEDGMENTS The China Scholarship Council supported the visit of Mr. Zhirong Shen to HR-Hydroscience and Engineering at The University of owa, and this help is deeply appreciated. We also thank for HR-Hydroscience and Engineering for hosting Mr. Zhirong Shen s visit for one year. Computations were performed at the Helium HPC cluster at The University of owa. This work is also supported by National Natural Science Foundation of China (Grant Nos and ), the National Key Basic Research Development Plan (973 Plan) Project of China (Grant No. 2013CB036103), High Technology of Marine Research Project of The Ministry of ndustry and nformation Technology of China, the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai nstitutions of Higher Learning (Grant No ), and Lloyd s Register Foundation (LRF), a charitable foundation, helping to protect life and property by supporting engineering-related education, public engagement and the application of research. REFERENCES [1] Carrica P. M., Wilson R. V., Noack R. W., and Stern F., 2007, Ship motions using single-phase level set with dynamic overset grids, Comput. Fluids, 36(9), pp [2] Shen Z., and Wan D., 2013, RANS computations of added resistance and motions of a ship in head waves, nt. J. Offshore Polar Eng., 23(4), pp [3] Simonsen C. D., Otzen J. F., Joncquez S., and Stern F., 2013, EFD and CFD for KCS heaving and pitching in regular head waves, J. Mar. Sci. Technol., 18(4), pp [4] Sadat-Hosseini H., Wu P.-C., Carrica P. M., Kim H., Toda Y., and Stern F., 2013, CFD verification and validation of added resistance and motions of KVLCC2 with fixed and free surge in short and long head waves, Ocean Eng., 9, pp [] Carrica P. M., Sadat-Hosseini H., and Stern F., 2012, CFD analysis of broaching for a model surface combatant with explicit simulation of moving rudders and rotating propellers, Comput. Fluids, 3, pp [6] Noack R. W., 200, SUGGAR: a general capability for moving body overset grid assembly, 17th AAA Comput. Fluid Dyn. Conf., Toronto, Ontario, Canada. [7] Menter F. R., 2009, Review of the shear-stress transport turbulence model experience from an industrial perspective, nt. J. Comput. Fluid Dyn., 23(4), pp [8] Jasak H., 1996, Error analysis and estimation for the finite volume method with applications to fluid flows, Ph.D. thesis, mperial College. [9] Rusche H., 2002, Computational fluid dynamics of dispersed two-phase flows at high phase fractions, Ph.D. thesis, mperial College. [10] Carrica P. M., Huang J., Noack R., Kaushik D., Smith B., and Stern F., 2010, Large-scale DES computations of the forward speed diffraction and pitch and heave problems for a surface combatant, Comput. Fluids, 39(7), pp [11] Shen Z., Wan D., and Carrica P. M., 2014, Dynamic Overset Grids in OpenFOAM with Application to KCS Self-Propulsion and Maneuvering, Ocean Eng., Submitted. [12] Otzen J. F., and Simonsen C. D., 2008, Uncertainty assessment for KCS resistance and propulsion tests in waves, Lyngby. [13] rvine Jr M., Longo J., and Stern F., 2008, Pitch and Heave Tests and Uncertainty Assessment for a Surface Combatant in Regular Head Waves, J. Ship Res., 2(2), pp Copyright 2014 by ASME