Analysis of Factors Affecting Extreme Ship Motions in Following and Quartering Seas

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1 Analysis of Factors Affecting Extreme Ship Motions in Following and Quartering Seas Chang Seop Kwon *, Dong Jin Yeo **, Key Pyo Rhee *** and Sang Woong Yun *** Samsung Heavy Industries Co., td. * Maritime & Ocean Engineering Research Institute/KORDI ** Dept. of Naval Architecture and Ocean Engineering, Seoul National University *** Abstract Recently, researches have been conducted by ITTC to find rational mathematical model for prediction of capsizing. According to this research movement, ee s mathematical model(1997), which describes 6 DOF transient motions such as capsizing of a ship in regular waves is modified, and a mathematical model for prediction of capsizing in following and quartering seas is suggested. Based on the suggested model, factors affecting prediction accuracy of capsizing are analyzed through comparing simulation results with experimental results. Simulation results are compared with ITTC bench mark test results. The prediction of capsizing events shows good agreement with ITTC bench mark test results in case of rolling tests in beam seas and free running tests in stern quartering seas, even though calculated roll angles are larger than those of experimental results. With the simulation results, it is found that the effect of nonlinear manoeuvring terms on the prediction of capsizing events is negligible. Although consideration of eg effect on manoeuvring coefficients could decrease roll amplitudes, histories of roll motions still have large differences from experimental results. Keywords: Capsizing, Following seas, Quartering seas, Nonlinear manoeuvring coefficients, Skeg effect 1. INTRODUCTION Extreme ship motions such as capsizing have been studied for a long time, but their mechanisms have not yet been clearly discovered. To survey the mechanisms of capsizing, ee(1997) suggested a mathematical model which describes 6-DOF transient motions of a ship in regular waves. Recently, researches have been conducted by ITTC to find rational mathematical model for prediction of capsizing. Many researchers have been studied to find optimal mathematical model comparing to experimental results. Umeda(1999) investigated the effect of nonlinear manoeuvring coefficients on the prediction of broaching phenomena. Munif(000) investigated the effect of model DOF change on the prediction of capsizing. In this study, factors in the 6-DOF mathematical model were investigated based on the previous researches on extreme ship motions.. MATHEMATICA MODE.1. COORDINATES SYSTEM To describe a ship s 6-DOF motion, spaced fixed coordinate S x0 y0z0, inertial coordinate O xyz, and body fixed coordinate G x y z were selected. Fig. 1 Coordinates System Fig. 1 shows coordinates system for the description of ship s 6-DOF motion. Positive z represents upward direction and the z = 0 plane represents undisturbed free surface. b b b Session A 45

2 .. EQUATIONS OF MOTION 6-DOF motions of a ship could be described based on Newton s nd law of motion. (Eq. 1) [ Inertia + Added Inertia][ = F INERTIA+ ADDED INERTIA + F GRAV Acceleration + F EXTERNA ] (1) Roll damping terms were calculated using Ikeda s (004) equivalent linear damping technique. = B eq φ Roll damping moment (4) B = B + B + B + B (5) eq F E BK.3. DESCRIPTION OF EXTERNA FORCES External forces, F external, acting on the ship could be classified into buoyancy, Froude-Krylov forces, diffraction forces, radiation forces, manoeuvring forces, rudder forces and thrust force. (ee, 1997) X = X + X + X F FK RUD T R Y = Y + Y + Y + Y + Y F FK DIF RAD MAN RUD Z = Z + Z + Z F FK DIF RAD K = K + K + K + K + K F FK DIF RAD RUD M = M + M + M F FK DIF RAD N = N + N + N + N + N F FK DIF RAD MAN DAMP RUD () 3. COMPARISON OF NUMERICA SIMUATION RESUTS WITH ITTC CAPSIZING MODE TEST RESUTS Model ship for the ITTC capsizing model tests is a 1/15 scale fishing vessel, Purse seiner. Table 1 shows principal dimensions of the model ship. Table 1 Principal dimension of fishing vessel Purse seiner model pp.3 m X CG m (aft) B m C B D 0.05 m KG 0.4 m T m GM m.3.1. Buoyancy & Froude-Krylov forces To calculate buoyancy and Froude-Krylov forces due to incident wave, incident wave pressure as well as static pressure was integrated up to an instantaneous free surface elevation along the ship surface..3.. Diffraction forces For the calculation of diffraction forces, velocity dependent term and acceleration dependent term were calculated separately based on the idea that diffraction forces could be divided into two components which are related to velocity and acceleration, respectively. (ee, 1997) Fig. Body plan of Purse seiner 3.1. CONSIDERATION OF SKEG EFFECT Because the model ship Purse seiner has large eg at her aft body, its effect should be considered. Fig. 3 shows the eg of Pulse seiner Radiation forces Impulse-response functions were adopted for the consideration of memory effect in time domain Manoeuvring Forces Eq. (3) shows mathematical models for the description of the forces due to ship manoeuvr. Manoeuvring coefficients were calculated using the empirical formula suggested by Kijima(1990). 1 Y ' v' + Y ' + Y ' v' v' + Y ' + v r vv rr Y ( v, r) = ρdu Ho ( Y ' v' + Y ' ) v' vvr vrr 1 N ' v' + N ' + N v r vv N ( v, r) = ρ du Ho Roll damping ' v' v' + N ' ( N ' v' + N ' ) v' vvr vrr rr (3) Fig. 3 Skeg of Purse seiner The effect of eg was contained in the mathematical model by two ways Skeg effect on roll damping The eg effect on roll motion was considered as roll damping force. Because the roll damping due to eg is assumed to be similar to that of bilge keel, empirical Session A 46

3 formula for bilge keel damping was adopted for the estimation of eg damping force. can be found in the figure, the result by present calculation coincides well with the Ayaz s (003) result. B = B + B SK SKN SKH (6) 8 3 B = ρ r b ω R f C SKN cb SK o D 3π (7) B SKH = 4 ρ r 3π cb b SK.5 1. D ω R f o π r f Ro A + 1.B (8) Skeg effect on manoeuvring forces Considering mathematical model for the fin effect on manoeuvring equations of motion (ewis, 1989), sway force and yaw moment produced by the eg were modeled as in Eq. (9). Y = ( cosβ + Dsin β ) N = Y x Where and eg. of eg from midship. (9) D are the lift and drag forces on the x is distance β is angle of attack of eg and Fig. 4 GZ curve 3.3. COMPARISON OF RO DECAY TEST Fig. 5 shows the comparison of roll decay test between numerical simulations and ITTC experiment results. Graph on left hand side shows roll decay history without forward speed and the graph on right hand side shows that of with forward speed of Froude number 0.. In each case, numerical simulations were found to estimate roll decay test results properly, especially in its magnitude. Manoeuvring coefficients for eg were wriien as Eq. (10). C ( Yv) = ( Yβ ) ( ) = ( ρ /) AV{( ) + ( Cd) } v C ( ρ /) A V ( ) ( Nv) = x ( Yv) (10) ( Yr) = x ( Yv) ( N ) = x ( Y ) r v Where A is area of eg, and C / β is; C = ( π /) a a = aspect ratio (11) Manoeuvring coefficients which included the eg effect were written as follows. Fig. 5 Comparison of roll decay test 3.4. COMPARISON OF 3 PORT TURN Fig. 6 shows the comparison of 3 port turn between numerical simulations and ITTC experiment results. The graph on left hand side shows roll angle history and the graph on right hand side shows yaw angle history. As could be found in the figure, estimated heel angle of numerical simulation is less than that of model test result by about. Simulated yaw angle gives reasonable estimates with the model test result. 1 π To B Y = ρtv 1.4C ( Y ) To Nv = ρ TV o ( Nv) + 1 To π Yr = ρtv o ( Yr) To To N = ρtv N v o B v ( ) r o r (1) Fig. 6 Comparison of Turning test result 3.. COMPARISON OF GZ CURVE Fig. 4 shows the comparison of GZ curve between Ayaz s (003) result and present calculation result. As 3.5. COMPARISON OF FREE RUNNING TEST (H/λ=1/15, λ/=1.5) Figs. 7 ~ 9 show the result of roll angle and yaw angle Session A 47

4 at Froude number 0., 0.3, 0.4, respectively. In each figure, incident wave direction is for upper, 1 for the middle, and for bottom graph, respectively. Although numerical simulation results over-estimate roll and yaw angle magnitude, numerical simulation could predict well whether the ship would capsize or not. Fig. 9 Comparison of Free run test result (Fn=0.4) Fig. 7 Comparison of Free run test result (Fn=0.) 4. EFFECT OF MODE VARIATION 4.1. EFFECT OF NONINEAR MANOEUVRING TERMS ON CAPSIZING PREDICTION Table shows the effect of nonlinear manoeuvring model on capsizing prediction. It can be found that the nonlinear manoeuvring terms give negligible effect on capsizing prediction. Therefore, it can be concluded that capsizing could be properly predicted with linear manoeuvring model. Table Effect of nonlinear manoeuvring model Fn Heading angle (λ/=1.0) 0.0 (λ/=1.5) Model test inear Nonlinear manoeuvring manoeuvring model model 0. 1 Fig. 8 Comparison of Free run test result (Fn=0.3) Session A 48

5 0.4 Capsize Capsize Capsize 1 Capsize Capsize Capsize Capsize Capsize Capsize 4.. EFFECT OF SKEG 4..1 Effect of eg roll damping model on capsizing prediction Table 3 Effect of eg roll damping model Fn Heading angle Model test (λ/=1.0) 0.0 (λ/=1.5) 0. 1 W/ Skeg roll damping W/O Skeg roll damping Capsize Table 4 Effect of sway force & yaw moment due to eg Fn Heading angle Model test 0.0 (λ/=1.0) (λ/=1.5) W/ Skeg effect W/O Skeg effect Capsize Capsize Capsize 1 Capsize Capsize Capsize Capsize Capsize Capsize Capsize 15 Fn 0. and 5 degree 10 Capsize 5 Capsize Capsize Capsize Roll angle Capsize Capsize Capsize -10 Capsize Capsize Capsize Table 3 shows the effect of roll damping due to eg on capsizing prediction. As is shown in the table 3, it can be concluded that eg roll damping should be considered for the prediction of capsizing Effect of manoeuvring force and moment due to eg on capsizing prediction Table 4 shows the effect of eg sway force and yaw moment on capsizing prediction. In the view point of capsizing, eg sway force and yaw moment enhance the capsizing prediction performance. And it was found that consideration of manoeuvring coefficients due to eg decrease the over-estimated roll and yaw angle. Figs. 10 and 11 show the comparisons of time histories of roll and yaw angle at Froude number 0. and incident wave angle. Yaw angle -15 w/ eg manoeuvring coeff w/o eg manoeuvring coeff ITTC result Time [sec] Fig. 10 Comparison of roll angle history Fn 0. and 5 degree -10 w/ eg manoeuvring coeff -15 w/o eg manoeuvring coeff ITTC result Time [sec] Fig. 11 Comparison of yaw angle history Session A 49

6 5. CONCUSION In this study, a mathematical model for prediction of capsizing in following and quartering seas was suggested, and the effects of nonlinear manoeuvring terms, roll damping moment due to eg, and sway and yaw manoeuvring forces due to eg were investigated. Nonlinear manoeuvring coefficients of the suggested model were calculated using the empirical formula suggested by Kijima(1990). For the modeling of eg effects, Ikeda s empirical formula of roll damping was adopted, and eg sway force & yaw moment due to eg were modeled considering the mathematical model of fin effect (ewis, 1989). Based on the suggested model, numerical simulations were conducted and simulation results were compared with the test results of ITTC bench mark ship, Purse seiner fishing vessel. Through the comparisons of GZ curve, roll decay test, 3 port turn, and free running test, overall estimation performance of the suggested mathematical model was surveyed. Through numerical simulations, it could be concluded that the suggested mathematical model could give reasonable estimates of the capsizing events of a ship. Even though numerical simulation over-estimated the roll and yaw angular displacements, numerical simulation could predict well whether the ship would capsize or not. By the consideration of roll damping due to eg, and sway force and yaw moment due to eg, over-estimated roll and yaw angle could be suppressed. Quartering Seas" Osaka University Ph. D. Dissertation, 000 UMEDA, N., "Nonlinear dynamics of ship capsizing due to broaching in following and quartering seas", Journal of Marine Science and Technology, Vol. 4, pp. 16-6, 1999 REFERENCE AYAZ, Z., SPYROU, K.J., VASSAOS, D., An Improved Numerical Model for the Study of Controlled Ship Motions in Extreme Following and Quartering Seas, The Proceedings of IFAC Conference on Control Application in Marine Systems, Glasgow, UK, 001 AYAZ, Z., Manoeuvring behaviour of Ships in Extreme Astern Seas, Department of Naval Architecture and Marine Engineering, Universities of Glasgow and Strathclyde, Ph. D. Dissertation, 003 IKEDA, Y., Prediction Methods of Roll Damping of Ships and Their Application to Determine Optimum Stabilization Devices, Marine Technology, Vol. 41, No., pp , 004 KIJIMA, K., NAKIRI, Y., TSUTSUI, Y., MATSUNAGA, M., Prediction Method of Ship Manoeuvrability in Deep and Shallow Water, MARSIM & ICSM 90, Tokyo, Japan, 1990 EE, H., Analysis of Dynamic Stability of a Ship in Regular Waves, Master s thesis, Seoul National University, 1997 EWIS, E. V., PRINCIPES OF NAVA ARCHITECTURE, The Society of Naval Architects and Marine Engineers, Volume 3. pp 34~38, 1989 MUNIF, A., "Numerical Modeling on Extreme Motions and Capsizing of an Intact Ship in Following and Session A 50

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