Computation and Experiment of Propeller Thrust Fluctuation in Waves for Propeller Open Water Condition

55 Computation and Experiment of Propeller Thrust Fluctuation in Waves for Propeller Open Water Condition by Emel Tokgoz *, Member Ping-Chen Wu *, Member Sumire Takasu **, Member Yasuyuki Toda *, Member Summary The prediction of the propeller load fluctuations in waves, which can cause great fluctuations of engine power and revolutions, is important for ship operations. Recently the prediction of free running model advancing in waves with real rotating propeller and rudder can be done by Computational Fluid Dynamics (CFD) technique. However, the validation of these methods is not enough and it requires huge mesh density and long computational time. The new propeller body-force prediction model (OU propeller model) was proposed in particular to make the computation of free running condition easier and applied for many problems. The present work is conducted to validate the capability of OU propeller model for the condition that propeller exists near free surface in waves. For the simulations, the Reynolds Averaged Navier-Stokes (RANS) solver CFDSHIP-IOWA V4.5 is used. The propeller loads are predicted, and validated against the existing experimental data and the experiments conducted in Osaka University towing tank. The results showed that the OU propeller model works well for moderate loadings and high expanded blade area ratios. 1. Introduction Under certain ship operating conditions, its propeller can emerge from the water and pierce the free surface. For instance, when a commercial ship like KVLCC2 (KRISO very large crude oil carrier 2) tanker advancing in long waves in ballast condition, its propeller would be out-of-water occasionally in one wave encounter period 1), 2). Based on viscous flow simulation and S-PIV (Stereo Particle Image Velocimetry) measurement, it is because of shallower stern draft compared to draft in fully-loaded condition and large vertical motions of stern in long waves. Moreover, this causes a sudden loss of propeller loads and fluctuation of engine revolutions, which is called propeller racing. Sadat-Hosseini 3) studied the instability of ONR tumblehome appended with twin rudder and twin propeller. It capsizes with high possibility when parametric roll resonance, broaching, bow diving or stability loss occurs in certain combination of wave heading, length and ship speed condition. During the ship rolls to a large angle and one of its twin-screw propeller emerges from water. Thus, estimating propeller performance while it is surface piercing is essential. However, when the propeller is operating at high loadings near the free surface, heavy sea states or surface-piercing, ventilation occurs. It is a very complicated phenomenon although it has been studied for long time. Many numerical studies have been carried out to study the performance of a propeller near free surface, even piercing it. Califano 4) used the commercial RANS * Department of Naval Architecture and Ocean Engineering, Osaka University ** Lloyd s Registration (Graduate School of Engineering, Osaka University while present research) Received 6 March 2017 code Fluent to investigate propeller ventilation mechanism using unstructured grid, multiple reference frame model, and sliding mesh. The free surface is modelled by VOF (Volume of Fluid) method. The SST k-ω turbulence model was used in open water test but turned off in free-surface simulation. The immersion depth ratio of propeller was I/R=1.4 where the propeller is fully submerged under undisturbed water surface. The predicted thrust and air content showed good agreement with the filtered experimental data for the first half revolution. Kozlowska 5) studied the propeller ventilation numerically and experimentally for different submergence cases, including surface-piercing propeller. The computations are carried out by TUHH and the free surface is modelled by VOF technique. The experiments are done in MARINTEK towing tank. The thrust ratio comparisons showed that for non-ventilating regime, the agreement is good between the calculations and the experiments. However, for the ventilating regime especially for high loading cases, CFD generally overpredicts the propeller forces. Also, the effect of ventilation on thruster loadings is investigated experimentally by Koushan 6). Carrica 7) studied broaching problem of fully appended ONR tumblehome in following waves using CFDSHIP-IOWA and overset grid topology. The free surface is modelled by single phase level set method. The twin propellers rotation direction was inward. The twin rudders were controlled by a PI controller. 6 DOF (Degree of Freedom) ship motions were validated against experiment results. As the ship turns to starboard and rolls to portside, starboard thrust decreases while getting closer to the free surface and then becomes unstable, eventually sudden thrust loss occurs. Also, when the ship is drifting with rolling, the bilge keel vortex would hit portside propeller which causes a thrust increase. Finally, it stayed constant with increased water depth and more uniform inflow. For future study, coupling PUF-14 or PUF3A in CFD to consider the cavitation and ventilation was proposed. Smogeli 8) provided an empirical ventilation thrust loss model for

56 日本船舶海洋工学会論文集第 25 号 2017 年 6 月 an open propeller. It is a function of relative shaft speed and immersion depth ratio. Many viscous flow computations using real propeller geometry in open water condition or appended to a ship have been performed 4), 9), 10). However, those kind of computations are very expensive due to huge mesh density and complicated grid generation. On the contrary, Osaka University proposed the new propeller body-force prediction model (OU propeller model) based on time averaged effect using total velocity field directly from viscous flow solver 11). Since the induced velocity subtraction is not required, the free surface modelling can be coupled with OU propeller model effortlessly 12). For the existed propeller program based on potential flow theory, negative image method (mirror effect or double body model) is necessary to consider the induced velocity from the free surface 13). Also, the OU propeller model had been applied and validated for several self-propelled ships like Series 60 14), 15) KVLCC2 16) and JBC 17) in calm water and KVLCC2 18) in regular head waves as well. They were in fully-loaded condition or with design draft, i.e. the propeller is far away from the free surface. The present work is to investigate the propeller performance numerically and experimentally considering the free surface effect in calm water and regular head waves. The simulations are validated against the existing experimental data 19) for MAU propeller and the experiments conducted in Osaka University towing tank for KVLCC2 propeller. The viscous flow simulations using discretized propeller geometry will be performed for limited cases to observe the detailed phenomena and provide correction for OU propeller model. For behind-hull condition, the self-propelled KVLCC2 tanker free to heave and pitch in ballast condition was simulated in regular head waves; λ/l=0.6, 0.9 and 1.5 2). Herein, additional results showing the comparison of the propeller thrust time history and ship motion responses between experiments and simulations are presented. Finally, the propeller model will be improved and further employed in various ship applications. 2. CFD and EFD Method 2. 1 Model Propellers and Test Conditions The computations are performed for two different type of propellers. One is five bladed MAU type propeller for a container ship, which is the same model as the one used for studying the propeller characteristics at racing condition in waves by Naito 19). The other is the four bladed propeller for 3.2 m KVLCC2 model tanker. The principle particulars of both propeller models are given in Table 1 below. The MAU type propeller has constant pitch (pitch ratio of 1.007) and KVLCC2 model propeller has variable pitch (pitch ratio at 0.7R is 0.7212). Fig. 1 displays right-handed propeller models for both types. The KVLCC2 model propeller has lower expanded blade area ratio compared to MAU type propeller. In Table 2, test conditions for computations of the MAU type propeller is listed. The open water experiments for this propeller were carried out by Naito 19) in calm water with varying propeller immersion and in regular waves of different wave heights with shallow immersion depth as listed in Table 2. The open water computations were done by Tokgoz 12) in calm water for various propeller immersions and the results were compared with experimental results. In this study, computations are conducted for three advance coefficient values with different wave amplitudes (A) at immersion depth ratio of I/R=1.2. In each simulation case, encounter wave frequency is constant and same, and propeller revolution is 10 rps. The non-dimensionalized number of revolutions, which is nd=nl/u0, used in the computations. Wavelength ratios are λ/l=1.31, 1.50 and 1.59 for low to high advance ratios, respectively. For the simulations of MAU propeller, Re and Fr are determined based on ship length L=4.8 m. The time increment is taken as Δt=0.003738. Table 1 Principle characteristics of model propellers Propeller model MAU KVLCC2 Diameter - D (m) 0.15 0.0986 Pitch ratio 1.007 0.7212 (0.7R) Expanded blade area ratio (EAR) 0.6935 0.431 Rotation direction Right Right Boss ratio 0.1848 0.155 Number of blades 5 4 Blade thickness ratio 0.0530 Fig. 1 MAU type propeller (Left) and KVLCC2 model propeller (Right) Table 2 Test conditions for CFD of MAU type propeller Propeller Case immersion J Wave (I/R) Regular 0.3 (n=10 rps) A=0.029 m waves 1.2 0.5 (n=10 rps) A=0.073 m ɷe=3.58 (1/s) 0.6 (n=10 rps) A=0.042 m The open water experiments for KVLCC2 model propeller are carried out in the towing tank of Osaka University. The model propeller is mounted in front of a submerged housing, which is towed by the carriage. The rotational speed is provided by a motor through the shaft pointing towards upstream. For thrust and torque measurement, a dynamometer set is equipped on the shaft. A wave gauge is installed in front of the carriage. The regular head waves are generated by the plunger-type wave maker at the tank head. The wave absorber is a small fixed gridiron beach at the tank end with movable beaches along its sides. The open water tests in calm water are done for J=0 to J=0.7 for various immersion depths as summarized in Table 3. The experiments in regular head waves are completed at immersion depth ratios I/R=1.2, 2.0 and 3.39 for three selected advance coefficients as listed in Table 3. The wave amplitude is A=0.019 m for all cases

Computation and Experiment of Propeller Thrust Fluctuation in Waves for Propeller Open Water Condition 57 and for I/R=2.0 case an additional wave amplitude is selected as 0.028 m. For I/R=1.2 and 2.0, wavelength ratios are λ/l=1.5, 1.0 and 0.6 (where L=3.2 m KVLCC2 model ship length). And for the deepest case (I/R=3.39), the wave length ratio equals to 1.0. The propeller number of revolution is 30 rps for all KVLCC2 model propeller cases. The carriage speed is changed for varying J values in the experiments. For the simulations of KVLCC2 model propeller, Re and Fr are determined based on ship length L=3.2 m. All the variables and properties are non-dimensionalized by ship length, the water density ρ, free-stream velocity and their combinations. Kinematic viscosity of water is assumed to be 10-6 m 2 /s and acceleration of gravity (g) is taken as 9.81 m/s 2. The computations are done for J=0.15 to J=0.7 for calm water cases. Fig. 2 Computational domain and boundary conditions. Table 3 Test conditions for KVLCC2 model propeller Case Propeller J Wave immersion (I/R) Calm water 3.39, 1.2, 1, 0.5 0 ~ 0.7 - (n=30 rps) 1.2 A=0.019, Regular 0.2, 0.35, 0.5 0.028 m waves 2 (n=30 rps) A=0.019 m 3.39 A=0.019 m 2. 2 Grid Generation Fig. 2 shows the computational domain and boundary conditions used in the simulations. The grid is generated by Gridgen software as Cartesian static overset grid. The computational domain consists of two independent blocks, one is background grid to capture the waves and the other is propeller grid block for propeller body-force calculations. The propeller grid block is illustrated with grey colored box in Fig. 2 below. Depending on propeller immersion depth, propeller block was relocated in z direction. The overset domain connectivity is obtained by Suggar code 20), so rebuilding new grids requires less effort. The overlapping part of grids is shown in Fig. 3 at I/R=1.2. The grid on the propeller plane is built fine enough to calculate the propeller loads accurately, 50 grid points are used per propeller diameter in y and z directions. Likewise, the grid is generated carefully around the free surface to capture the waves precisely. At least 11 grid points are used per wave amplitude in z direction and 45 grid points are used per wavelength in x direction. In total, nearly 3,45 M (million) grid points are used. The computational domain extends from -0.24<x/L<1.75, -1.0<y/L<1.0 and -0.79<z/L<0.22. The z-axis is positive in upward direction and y-axis is positive in starboard direction. The propeller plane is located at x/l=0 and the undisturbed free surface is at z/l=0. The far field boundary conditions are implemented for the top and bottom of the background domain. For the inlet, wave boundary condition calculated from the linear potential flow solution is applied. The exit boundary condition is used for the outlet and zero gradient condition is implemented for the side boundaries. Fig. 3 Overlapping grid system at I/R=1.2. 2. 3 Computational Outline The simulations are carried out with URANS (Unsteady Reynolds-Averaged Navier Stokes) solver CFDSHIP-IOWA that uses multi-block structured grid with overset gridding capability to simulate the flow field around complex geometries. Herein, SST k-ω turbulence model is used for turbulent viscosity. The free surface is modelled by using a single phase level set method. Only the water side of the flow field is computed and for satisfying the kinematic and dynamic free surface boundary conditions, jump conditions are imposed at the free surface. These conditions result in equations for extension velocities in the air side, and in pressure interpolations to satisfy atmospheric pressure at the free surface 21). For discretization of time, convective and viscous terms second-order finite difference methods are utilized. For the time derivatives near the free surface, a Lagrangian/Eulerian approach is used 21). The projection method is used for the velocity-pressure coupling. In this study, the OU propeller model, which is proposed by Tokgoz 11), is employed as an interactive propeller model. The model is based on quasi-steady blade element theory using the CFD total velocities (u/u0, v/u0, w/u0) on propeller plane to calculate the thrust and torque distributions in infinite blade assumption. The time averaged body-forces on the propeller plane are calculated using the time averaged local pressure jump and added as the source terms in the momentum equations of URANS solver. The chord, pitch and thickness distribution along the propeller radius are considered in the computations. While predicting the local thrust and torque acting on representative blade element, the two dimensional lift coefficient (CL) and drag

58 日本船舶海洋工学会論文集第 25 号 2017 年 6 月 coefficient (CD) are utilized. CL is estimated by CL=2πk1sinα, where k1 is a correction factor to include blade to blade interaction and α is the angle of attack against zero-lift line. CD is assumed as 0.02 for KVLCC2 model propeller and 0.01 or by an empirical formula introduced by Moriyama 22), which takes into account the blade thickness, for MAU type propeller. The details of the OU propeller model and time averaged body-force calculations are explained by Tokgoz 11), 12). 3. Results 3. 1 MAU Propeller For MAU type propeller in calm water, the thrust and torque coefficient (KT, 10KQ) show good agreement between CFD and EFD except for higher loading region J>0.3 12), as shown in the Appendix (Fig. A1 and Fig. A2). Even if, within CFD code in OU propeller model, the propeller wet area ratio is interacting with free surface, it could not predict the thrust loss due to ventilation effect. Thus, KT and 10KQ are overestimated for lower J. In higher J region, the ventilation effect is phased out by time averaged effect. Fig. 4 displays the propeller thrust coefficient fluctuations for different loading conditions in regular waves at I/R=1.2. It is the time histories of propeller wet area ratio, KT and incident wave amplitude. The wave amplitude is represented by red line, and the propeller wet area ratio is shown by green line. The blue line is the thrust coefficient fluctuation predicted by CFD, and black line is the experimental result. The dotted line shows the thrust coefficient in calm water for deepest case (I/R=3.39) predicted by CFD. between the inflow velocity and the propeller racing, from the experimental investigations 19). And, it might be caused by the free surface deformation or instability when increasing propeller suction is near the free surface. Under the wave trough, the propeller tip is out-of-the water, and the loss of effective disk area causes the lowest thrust. For this immersion depth in calm water, the open water characteristic curve shows the thrust coefficient drops suddenly for J<0.4, which can be a critical J for this propeller 19). For high loading as J=0.3, EFD shows much lower minimal KT with high frequency fluctuation since the ventilation mechanism is not modelled in CFD. The average KT in waves for all loading cases are lower than KT in calm water for deepest immersion depth (I/R=3.39), due to the free surface effect. Fig. 5 shows the CFD result of MAU propeller operating under the wave trough. The free surface elevation and axial velocity contours are displayed. As it is seen, at this immersion depth propeller pierces the free surface under wave trough. The solid black lines represent the free surface. The waves are deformed due to propeller body-force acting across the free surface. A small peak or jet forms behind the propeller and the wave trough becomes deeper on starboard side. For a surface-piercing propeller operating in calm water, the axial velocity increases also on the port side and the free surface deforms similarly close to the propeller plane due to the propeller rotation 12). The propeller wake is meandering as the wave propagates. Fig. 4 MAU type propeller thrust fluctuations in regular waves (λ/l>1). For low loadings as J=0.5 and 0.6, KT fluctuation shows good agreement between EFD and CFD. Both CFD and EFD KT fluctuation results include 2 nd harmonic components. For J=0.6, the variation of propeller loading is less than the case for J=0.5 for both results. When the propeller is fully submerged, under the wave crest, thrust drops. The nonlinear interactions of the propeller load components can be defined as effects arising from the change of propeller immersion and the phase difference Fig. 5 MAU type propeller operating at I/R=1.2 under wave trough. 3. 2 KVLCC2 Model Propeller Fig. 6 shows the images (top view) captured from the experiments of KVLCC2 model propeller in regular head waves at I/R=1.2. On the left, the propeller is fully submerged under the wave crest and on the right, the propeller tip is surface-piercing under wave trough. For both images, severe ventilation indicated by huge amount of air bubbles and sprays is observed. For KVLCC2 model propeller the ventilation is more violent due to the smaller EAR of propeller blade and higher propeller rotation number (n=30 rps) compared to MAU type propeller cases.

Computation and Experiment of Propeller Thrust Fluctuation in Waves for Propeller Open Water Condition 59 becomes more important. Highest values of thrust coefficient are calculated near the wave crest and the lowest values are measured close to the wave trough where the ventilation becomes significant. Fig. 6 Free surface around KVLCC2 model propeller at I/R=1.2 (left: at wave crest, right: at wave trough). The propeller open water characteristics in calm water for KVLCC2 model propeller at two immersion depths are shown in the Appendix (Fig. A3). The dashed lines demonstrate the OU propeller model results, the solid lines represent the experimental data. CFD and EFD have good agreement except for high loading region (J>0.4) for deepest case (I/R=3.39). The torque coefficient for EFD is greater than CFD results due to the increased drag caused by trip wires used on the propeller model blades. As seen in Fig. A2 at I/R=0.5, very clear rapid thrust loss occurs during the transition (e.g. J=0.4-0.5) from partial to full ventilation 23). For this propeller, the experiments show that for different immersion depths, the thrust drops suddenly when J<0.5. It is caused by severe ventilation induced by smaller EAR compared to MAU propeller. The smaller chord length would produce larger pressure difference or peak on the blade and then suck large amount of the air into the water. Therefore, since the ventilation mechanism could not be considered in CFD, the predicted values are generally overestimated. The same conclusion can be drawn for different I/R. The thrust coefficient fluctuations for KVLCC2 propeller in regular head waves for various immersion depths at different loading conditions are presented in Fig. 7 to Fig. 9. The horizontal axis is the non-dimensional time, the vertical axis on the left indicates KT and the right side axis corresponds to wave (red lines in the graph). The black lines are the results for the deepest case in calm water, the blue lines are for the deepest case in waves, the green lines represent the results at I/R=2.0 in waves and pink lines show the results at I/R=1.2 in waves. Fig. 7 displays the time series of propeller thrust coefficient for high loading condition, Fig. 8 is for J=0.35 and Fig. 9 is for J=0.5. For CFD and EFD, the average KT values in waves at I/R=3.39 for all loading cases are very close to the ones in calm water. On the other hand, mean KT values for CFD are slightly underestimated for deepest case, especially when J=0.2. Same conclusions can be drawn for I/R=2.0. The CFD results have slight difference between I/R=3.39 and I/R=2.0. As written at the section 2.2, the propeller block is relocated in z-direction with the different immersion depth. Therefore, the grid modification close to the free surface can cause difference in the calculations. Due to the wave orbital velocity, KT has its minimum value when the wave crest is at the propeller plane. However, when the immersion depth decreases the effect of propeller emergence Fig. 7 KVLCC2 model propeller thrust fluctuation in regular waves (λ/l=1.0, J=0.2). The mean CFD KT values in waves at I/R=1.2 is much larger than the EFD results for presented loading conditions. However, the greatest deviation is observed for high loading condition as seen in Fig. 7, supporting the calm water results. As it is also shown in Fig. 6, at this immersion depth the ventilation influence is severe and in CFD this complicated phenomenon is not considered. With the increased immersion depth of the propeller, thrust rises because of the reduction in ventilation. The time history of thrust coefficient for J=0.5 as presented in Fig. 9, shows less variation for immersion depth ratio of I/R=1.2 compared to the results for J=0.2 in Fig. 7. The propeller thrust was recorded for two different wave amplitude values at I/R=1.2 in the experiments. The EFD time history of KVLCC2 model propeller thrust fluctuation in regular waves at I/R=1.2 is shown in Fig. A4. In Fig. 9, pink line represents the thrust coefficient time series for wave amplitude A=0.019 m and brown line is for the A=0.028 m. It can be concluded from both figures that the wave amplitude has significant effect on propeller thrust at this loading condition. Higher wave amplitude causes larger thrust loss. Thrust values suddenly drop when the wave trough reaches to propeller plane where the ventilation increases. Fig. 8 KVLCC2 model propeller thrust fluctuation in regular waves (λ/l=1, J=0.35).

60 日本船舶海洋工学会論文集第 25 号 2017 年 6 月 The thrust time history comparison between CFD and EFD in λ/l=0.6 is shown in Fig. 10. The horizontal axis is the non-dimensional time, the vertical axis is the thrust in N (newton) and wave elevation at the propeller plane in cm. In Fig.10, EFD thrust is lower than CFD one and has two different mean values, corresponding to region A and B shown in Fig. A5. The thrust fluctuation is not simple harmonic for CFD and EFD. The maximal thrust for CFD is predicted in the vicinity of wave trough. For EFD, thrust increases as wave trough comes. A sudden thrust loss appears right before the wave trough. While the propeller is very near free surface, thrust drops suddenly due to ventilation. CFD result could capture similar phenomena in longer waves such as λ/l=0.9, as shown in Fig.11. Fig. 9 KVLCC2 model propeller thrust fluctuation in regular waves (λ/l=1.0, J=0.5). 3. 3 Behind-Hull Conditions The propeller performance and ship motions of KVLCC2 tanker in ballast condition in regular head waves in λ/l=0.6, 0.9 and 1.5, were predicted by CFD 2). The OU propeller model was coupled with RANS solver and motion solver within the code. The details of the test conditions, ship and propeller geometry, experimental setup, methods used in the simulations and the grid topology were given by Tokgoz 2). In EFD, the ship is free to surge, heave and pitch and in CFD it is free to heave and pitch. The number of propeller revolutions was determined by self-propulsion test as n=18rps for λ/l=0.6, 30rps for λ/l=0.9 and 28rps for λ/l=1.5. In the simulations, n=18rps, which corresponds to J=0.448 for all λ/l. In the experiments severe ventilation effect to the propeller thrust was observed for λ/l=0.6 even though the propeller would not pierce the free surface. In Fig. A5 (in the Appendix), the time history of the ship motions and the thrust fluctuation are shown along with the wave elevation at the propeller plane. In the experiment, the measured wave amplitude has small deviations from the incident wave amplitude. It is very hard to keep the wave amplitude constant, especially for short waves. The thrust is sensitive to the wave amplitude as explained in Fig. 9. Fig. 11 The time history of thrust fluctuation in waves λ/l=0.9 (top: CFD n=18rps, bottom: EFD n=30rps). EFD result in same wave condition but with different n is illustrated below in Fig. 11. The thrust fluctuation shape of CFD is similar to EFD. For EFD, close to the wave trough, thrust drops sharper and faster than CFD. And, when the wave crest is at the propeller plane, thrust fluctuation includes higher harmonics in both results. Thrust amplitude is much larger for EFD than CFD. The propeller pierces the free surface under wave trough. And, the thrust decreases along with the reduction of the propeller wet area. The simulation result for λ/l=1.5 also shows the similar trend. In Fig. 12, 1 st harmonic amplitudes of heave (z1/a) and pitch motion (θ1/ka) for different λ/l are shown. The current CFD and EFD results are labeled with wprop in the graphs, which means with-propeller cases. The other data represent the without-propeller cases, which were obtained by Wu 1). There is a good agreement between the simulations and the experimental results. Besides, the ship vertical motions in waves are not affected by the propeller existence. The same conclusion was also drawn by Wu 18) for fully-loaded condition. Moreover, the ventilation phenomenon or surface piercing propeller effect have no significant influence on the ship vertical motions in waves. Fig. 10 The time history of thrust fluctuation in waves λ/l=0.6.

Computation and Experiment of Propeller Thrust Fluctuation in Waves for Propeller Open Water Condition 61 References Fig. 12 1 st harmonic amplitudes of heave and pitch motion for ballast condition (top: heave, bottom: pitch motion). 4. Conclusions The OU propeller model is coupled with RANS solver CFDSHIP-IOWA to predict the propeller loads in open water for two different propeller models. And some additional results are presented for behind-hull condition in ballast condition. The following conclusions are drawn according to the presented comparisons. The OU propeller model can be used for usual loadings of high EAR propeller near the free surface. For small EAR propeller, the model shows the overestimation of thrust due to the lack of ventilation phenomena on the blade surface. The variations of thrust are influenced by the free surface elevation. In open water, highest values of thrust for both EFD and CFD are observed in the vicinity of the wave crest, when the propeller submergence increases, and the lowest values are calculated close to the wave trough where maximum ventilation occurs. For behind-hull condition, the thrust fluctuations trends for CFD and EFD are similar for long λ/l. The maximum thrust is observed close to the wave trough and suddenly drops because of the ventilation. This reduction of thrust happens earlier and sharper in the experiments. The vertical ship motion responses revealed same trend for simulations and experiments. As a further study, modeling the ventilation effect is required to predict the racing conditions; by real propeller simulation the ventilation effect can be investigated. And, for KVLCC2 model propeller more experimental data in open water in waves for ventilated conditions are required. Acknowledgments This work was partially supported by JSPS KAKENHI Grant Number 24246142. 1) Wu, P. -C., Okawa, H., Akamatsu, K., Sadat-Hosseini, H., Stern, F. and Toda, Y.: Added resistance and nominal wake in waves of KVLCC2 model ship in ballast condition, In 30 th Symposium on Naval Hydrodynamics, Australia, 2014. 2) Tokgoz, E., Wu, P. -C. and Toda, Y.: Computation of the flow field around self-propelled ship in ballast condition in waves using body-force model, In Proc. of 3 rd International Conference on Violent Flows, Osaka, 2016. 3) Sadat-Hosseini, H., Carrica, P., Stern, F., Umeda, N., Hashimoto, S., Yamamura, S. and Matsuda, A.: Comparison CFD and system based methods and EFD for surf-riding, periodic motion, and broaching of ONR tumblehome, In 10 th STAB, pp. 317-330, 2009. 4) Califano, A. and Steen, S.: Analysis of different propeller ventilation mechanism by means of RANS simulation, In 1 st International Symposium on Marine Propulsors, Norway, 2009. 5) Kozlowska, A. M., Wockner, K., Steen, S., Rung, T., Koushan, K. and Spence, S. J. B.: Numerical and Experimental Study of Propeller Ventilation, In 2 nd International Symposium on Marine Propulsors, Germany, 2011. 6) Koushan, K., Spence, S. J. B. and Hamstad, T.: Experimental Investigation of the Effect of Waves and Ventilation on Thruster Loadings, In 1 st International Symposium on Marine Propulsors, Norway, 2009. 7) Carrica, P., Sadat-Hosseini, H. and Stern, F.: CFD analysis of broaching for a model surface combatant with explicit simulation of moving rudders and rotating propellers, Computers & Fluids, Vol. 53, pp. 117-132, 2012. 8) Smogeli, O. N.: Control of marine propellers from normal to extreme conditions, PhD thesis, Norwegian University of Science and Technology, 2006. 9) A Workshop on CFD in Ship Hydrodynamics, Vol. 2-3, Tokyo, 2015. 10) Sakamoto, N. and Kamiirisa, H.: Estimations of propeller cavitation noise by CFD conventional vs highly-skewed propeller. In Conference Proceedings of Japan Society of Naval Architects and Ocean Engineers, Vol. 21, pp. 317-332, 2015. 11) Tokgoz, E., Kuroda, K., Win, Y. N. and Toda, Y.: A new method to predict the propeller body-force distribution for modelling the propeller in viscous CFD code without potential flow code, J. of the Japan Society of Naval Architects and Ocean Engineers, Vol. 19, pp. 1-7, 2014. 12) Tokgoz, E., Wu, P. -C., Yokota, S. and Toda, Y.: Application of new body-force concept to the free surface effect on the hydrodynamic force and flow around a rotating propeller, In the 24 th ISOPE, pp. 607-612., 2014. 13) Young, Y. L. and Kinnas, S. A.: Analysis of supercavitating and surface-piercing propeller flows via BEM, Computational Mechanics, 32 (4), pp. 269-280, 2003. 14) Win, Y. N., Tokgoz, E., Wu, P. -C., Stern, F. and Toda, Y.: Computation of propeller-hull interaction using simple

62 日本船舶海洋工学会論文集第 25 号 2017 年 6 月 body-force distribution model around Series 60 CB=0.6, J. of the JASNAOE, Vol. 18, pp. 17-27, 2014. 15) Win, Y. N., Tokgoz, E., Wu, P. -C., Stern, F. and Toda, Y.: Computation of propeller-hull interaction using simple body-force distribution model around modified Series 60 CB=0.6 hull with hub, In the 24 th ISOPE, pp. 759-765., 2014. 16) Win, Y. N., Wu, P. -C., Akamatsu, K., Okawa, H., Stern, F. and Toda, Y.: RANS Simulation of KVLCC2 using simple body-force propeller model with rudder and without rudder, J. of the JASNAOE, Vol. 23, pp. 1-11, 2016. 17) Yokota, S., Wu, P. -C., Tokgoz, E. and Toda, Y.: CFD computation around energy-saving device of Japan Bulk Carrier on overset grid, In Conference Proceedings of JASNAOE, Vol. 21, pp. 313-316, 2015. 18) Wu, P. -C., Tokgoz, E., Okawa, H., Tamaki, K. and Toda, Y.: Computation and experiment of propeller performance and flow field around self-propelled model ship in regular head waves, In 31 st Symposium on Naval Hydrodynamics, California, 2016. 19) Naito, S. and Nakamura, S.: Open water characteristics and load fluctuations of propeller at racing condition in waves, J. of the Japan Society of Naval Architects and Ocean Engineers, 192, pp. 51-63, 1979. 20) Carrica, P. M., Wilson, R. V., Noack, R. W. and Stern, F.: Ship motions using single-phase level set with dynamic overset grids, Computers & Fluids, Vol. 36, pp. 1415-1433, 2007. 21) Carrica, P. M., Wilson, R. V. and Stern, F.: An unsteady single-phase level set method for viscous free surface flows. Int. J. Numerical Meth in Fluids, Vol. 53, pp. 226-256, 2007. 22) Moriyama, F.: On an approximate numerical method for estimating the performance of marine propellers, National Maritime Research Institute Report, Vol. 16, No. 6, pp. 361-376, 1979. 23) Young, Y. L. and Kinnas, S. A.: Performance prediction of surface-piercing propeller, Journal of Ship Research, Vol. 28, No. 4, pp. 288-304, 2004. Fig. A2 MAU model propeller open water characteristics (I/R=0.5). Fig. A3 KVLCC2 model propeller open water characteristics (top: I/R=3.39, bottom: I/R=0.5). Appendix Fig. A4 EFD time history of KVLCC2 model propeller thrust fluctuation in regular waves (I/R=1.2, λ/l=1.0, J=0.5). Thrust (N) wave-prop (cm) heave (cm) pitch (deg) surge (cm) Fig. A1 MAU model propeller open water characteristics (I/R=1.53). Fig. A5 EFD time history of KVLCC2 ship motions and thrust fluctuation in regular waves λ/l=0.6.