Water Entry Simulation of Free-fall Lifeboat

Transcription

1 193 Water Entry Simulation of Free-fall Lifeboat by Makoto Arai* Member M. Reaz H. Khondoker** Member Yoshiyuki Inoue* Member Summary Free-fall lifeboats provide a safe alternative to conventional lifeboats for emergency evacuation from ships and offshore platforms. The international regulations require that a lifeboat for free-fall launching shall be capable of rendering protection against harmful accelerations when it is launched with its full complement of persons and equipment from at least the maximum designed height. Through model and full scale tests, much has been studied about the behaviour of these lifeboats. These tests, however, are very expensive to conduct and the complete behaviour of the boat is sometimes difficult to discern. A mathematical model, therefore, can be very much effective to quantitatively evaluate the kinematics of the free-fall lifeboat. The hydrodynamic impact of the boat at water entry is a complex problem and is responsible mostly for the acceleration on board. Presented in this paper is a mathematical model where impact has been evaluated for a realistic lifeboat hull on the basis of the concept of a momentum theory, and the falling motion of the boat has been computed by solving the motion differential equations in the time domain. From the numerical simulation, trajectories of the boat and time histories of accelerations in different positions and directions are obtained. Model experiment has also been conducted to verify the numerical results and good agreement has been obtained between the numerical and experimental results. 1. Introduction All ships, mobile offshore drilling units and offshore platforms are required by regulatory agencies to have some types of emergency evacuation equipments on board. To date the most common lifesaving equipment is the conventional lifeboat. However, many life threatening accidents have occurred with this type of lifeboats during launch into water. This risk has substantially reduced due to the use of free-fall lifeboats recently. During the launch of a free-fall lifeboat there are two primary concerns. The first one is the motion of the lifeboat which is affected by the change in hull shape, weight distribution and initial conditions. The second one is the acceleration of the field to which the occupants in the lifeboat are subjected. Harmful accelerations may occur in the free-fall lifeboat when it impacts on the water. This hydrodynamic impact of the boat during water entry is a complex problem and makes the * Faculty of Engineering, Yokohama National University, Japan. ** Graduate School, Yokohama National University, Japan. Received 10th July 1995 Read at the Autumn meeting 16, 17th Nov establishment of the analytical method a challenging task. According to von Karman's1) momentum theory, when a body enters the water its original momentum be distributed between the body and the surrounding water. And the force acting on the body can be evaluated by the rate of change of momentum transfer to the surrounding water. He also approximated the added mass of a wedge shaped body as that of a flat plate with same length and width. Therefore, for a certain immersion the added mass of the wedge is equal to the mass of water contained in a semi cylinder having the length equal to the length of the wedge and the diameter equal to the wetted width of the wedge at that immersion. Similar approximation can be applied for the free-fall lifeboat with proper modifications. The boat has different shape for different sections, but it is possible to determine the wetted width at different immersion which in fact be used in this study to determine the added mass and impact force. Till now little work has been carried out regarding the whole process of free-fall lifeboat launching. Werenskiold2) presented a paper in the conference on Marine Survival Craft organized by RINA on the design of free-fall lifeboat systems and human aspects. Tasaki3)et al. performed a precise numerical calculation based on their mathematical model for the cases before the water entry. Nelson4) et al. developed a

2 194 Journal of The Society of Naval Architects of Japan, Vol. 178 numerical method of motion simulation considering the lifeboat as an integrated structure of a number of triangular plates. Boef5) developed a mathematical model for the whole launch procedure from the time the boat is released until it is in water. He computed the impact on the basis of the momentum theory and devised a numerical method of motion simulation for a uniform cross-sectional body. The authors') have done a basic work on the motion simulation of cylindrical bodies during water entry. Presented in this paper is an improved numerical method which can be used to predict the launch behaviour of realistic free-fall lifeboats for skid launching. Through comparison with model experimental data, the numerical method is shown to provide a reasonable prediction of the launch behaviour of free-fall lifeboats. 2. Launch Simulation of Free-fall Lifeboat The complete launch from the skid of a free-fall lifeboat is composed of four phases3), namely : sliding or ramp phase, rotation or restricted fall phase, freefall phase and water entry phase. The ramp phase is that phase of the launch when the boat slides along the skid and ends when the center of gravity of the boat passes a certain point very close to the end of the skid. At that time the lifeboat begins to rotate and slides about the end of the skid. The rate of the rotation increases until the boat is no longer in contact with the skid at which time the free fall phase begins. The free-fall phase ends when the bow first contacts the water. A fixed global system (x, z) is set with x-axis describing an axis along the still water level and z-axis corresponding to the vertical axis from the still water surface to the lowest end of the skid. A local coordinate system (E, ) is set with its origin at the center of gravity of the lifeboat at any time and instantaneous lifeboat axis describes $ axis. Both coordinate systems, as shown in Fig. 1, are right handed orthogonal Cartesian coordinate systems. The local coordinate system Fig. 1 Parameters of free-fall launching is used to describe the geometry of the lifeboat and to determine the forces that act on the lifeboat. The global coordinate system is used to set the governing equations for time step simulation. The local coordinate system, which is fixed in relation to the lifeboat, translates and rotates with respect to the global coordinate system Sliding phase Sliding of the boat begins when it is released and ends when the centre of gravity (G) is crossing a point close to the end of the launch skid. During this phase the lifeboat is constrained to slide along the skid, so it cannot rotate. The forces acting on the lifeboat during sliding are the gravity force (Mg), the normal reaction force (Fn) between the skid and the rail, and the frictional force (Đfn) between the skid and rail. The governing equations are based on the global coordinate system which provides three degrees of freedom and are given as : (1 ) (2 ) In Equations ( 1 ) - ( 3 ), M is the mass of the lifeboat, I is the rotational moment of inertia for pitching, Đ= (3 ) tan ė is friction factor and 0 is the instantaneous angle of the axis of the boat with horizontal Rotation phase The rotation phase of the free-fall launch begins as the sliding ends and it continues until the boat is no longer in contact with the launch skid. The forces acting on the lifeboat during rotation are the gravity force (Mg), friction (Đfn) parallel to the launch rail, and a force normal to the rail (Fn). A couple is produced by the weight of the boat and the reactive force on the launch rail, and it causes the boat to rotate as it slides off the launch skid. The equations of motion are : ( 4 ) (5 ) (6 ) 2. 3 Free-fall phase The free-fall phase of the launch begins at the end of the rotation phase and continues until the boat touches the water surface. During free falling of the boat the only force acting on the boat is its gravity force (Mg) and hence the equations of motion are simple. ( 7 ) (8 ) (9 ) Except for conditions with large fall heights and high wind speeds, the influence of the air drag is insignificant. Including this influence results in only a decrease of vertical momentum due to the gravity force. The horizontal and angular velocities of the boat remain almost constant. The rotation of the boat during the free fall is very important as it determines the angle of attack at water entry.

3 Water Entry Simulation of Free-Fall Lifeboat Water entry phase The water entry of the free-fall lifeboat begins at the end of the free-fall phase. During the water entry phase, the boat is acted upon by hydrostatic and hydrodynamic forces and the equations of motion can be given as : (10) (11) (12) Here, Fmn is the force due to momentum transfer in the normal direction to the boat axis, Fma is the force due to momentum transfer in the axial direction, Fdn, normal drag force, Fda, axial drag force, Fb, buoyancy force, Mg, gravity force, Mmn, moment due to momentum transfer in the normal direction, Mdn, drag moment and Mb, buoyancy moment. Numerical integration of these equations to obtain acceleration, velocity and displacement of the boat are performed by Newmark a method. 3. Calculation of Hydrostatic and Hydrodynamic Forces and Moments Because there is a detailed description3) about the forces acting on the boat in the first three phases, we show only the hydrostatic and hydrodynamic forces which are necessary to simulate the behaviour of the boat in the water entry phase. The volumetric force, the normal drag force and the force due to momentum transfer in normal direction have been calculated using a strip model : the forces per cross-section are calculated using the relative velocity and acceleration, and they are integrated over the length of the falling boat. To perform the numerical integration, the boat has been discritized into fourty segments in the longitudinal direction, since discritization into fewer segments (eg., twenty segments) gives coarse results in the calculation of normal accelerations. The forces along the axis of the boat has been approximated in total. The buoyancy force is proportional to the immersed volume of the body. This volume can be obtained by integrating the immersed cross-sectional area A1(E) along the length of the boat. The total volumetric force and its moment around the center of gravity of the boat become : (15) (16) (17) Where, 2cm is the maximum breadth of the boat at each cross-section, Acm is the cross-sectional area of the midship and vax and vnr are the axial and normal velocity and these can be given by the following equations : (18) (19) The drag forces in Equations (15) - (17) are based on the cross-flow principle which assumes that the incident flow can be split into orthogonal components which are independent of each other. The axial drag coefficient (Cda) depends on both skin friction and end pressure whereas normal drag coefficient (cdn) is dominated by pressure drag. The drag coefficients for axial and normal flow have been chosen from Hoerner7) Impact Formulation : The hydrodynamic force due to momentum transfer in the normal direction to the axis of the boat has been formulated on the basis of the momentum theory) and assuming irreversible nature of the impact. The force on an arbitrary cross-section at position E with length de (see Fig. 2) can be given as : (20) Where dm/dt, the time derivative of added mass m(e, h) for a particular section located at a distance E from the center of gravity and having an immersion h, is (21) But dh/dt will be evaluated only when vnr >0, which corresponds to conditions of increasing immersion. When vnr < 0, dh/dt is set equal to zero. This treatment') is based on considerations of momentum transfer only upon water entry and not during conditions associated with water exit. The total force due to momentum transfer in the (13) (14) In Equations (13) and (14), p is the density of water, of gravity of the boat. The hydrodynamic drag forces and moment in the local moving coordinate system have been computed using the following equations : Fig. 2 Water entry parameters of a free-fall lifeboat

4 196 Journal of The Society of Naval Architects of Japan, Vol. 178 normal direction can be obtained by integrating the force as described in Equation (20) throughout the length of the boat. The force and moment due to momentum transfer in the normal direction around the center of gravity of the boat then become : (22 ) (23 ) During water entry, the bottom of the front part of the boat first hits the water surface with velocity vax axially. At that time vax tan a, the component due to axial velocity (vax) and longitudinal bottom shape (tan a, a is the instantaneous angle of the bottom with axial direction ) of the front part of the boat, added some extra force in normal direction. This force causes rotation of the boat when it moves even with axial velocity only. Including this effect the equations for force and moment due to momentum transfer in the normal direction to be modified as : (24 ) (25 ) The added mass per unit length m(e, h) in Equation (22) and (23) and its derivative am/ah are functions of the immersion h(e) of the keel of the boat from the still water level. The immersion h(e) can be expressed as : (26 ) The distribution of added mass m(e, h) and its time derivative for different immersion have been evaluated according to the following relations (Fig. 3) : (27 ) (28 ) where c(e, h) is the instantaneous wetted half-width of a particular section at immersion h and cm(e, d1) is the maximum half-width at immersion di. The derivative Fig.3Accelerometer positions and immersion parameters separation from the body during water entry of the lifeboat (see Fig. 4). Since different cross sections have different shape and size, input data for those sections have been extracted from the body plan of the lifeboat model. A transverse section has been divided into a number of equally distant ordinates and for the immersion between two consecutive ordinates, the wetted half-- width is calculated by linear interpolation. For the momentum transfer along the boat axis, similar approach has been adopted but the force has been approximated in total. The average acceleration between the bow and center of gravity has been used. The force associated with the axial momentum transfer is : (29 ) Here, Lf is the distance between the fore peak and the center of gravity of the lifeboat, m(l) is the axial added mass and dm/dl is its derivative, which depend on axial immersion 1 ( Fig. 2). Moreover, in Equation (29), dl/dt is set equal to zero when vax< 0,i.e., the momentum transfer is evaluated only for advance of the boat and not for backward motion. The axial immersion 1 and the distribution of axial added mass m(1) are : for l< L/2 for l>l/2 (30 ) (31 ) (32) The added mass distribution function in Equation (31) is taken roughly from the change of the sectional area in the fore part of the boat, and max, the axial added mass for full immersion, has been taken on the basis of the added mass for an ellipsoid which is : (33) where L is the length of the boat, D=(ch+d2) at midship of the boat and k is a coefficient depending on the LID ratio. According to the above approximation for axial immersion and added mass, the computed axial acceleration increases suddenly at the time the axis of the boat touches the water surface. However, the axial impact should occur as soon as the keel of the boat touches the water surface and gradually increase to the peak value. Therefore, a different added mass approximation has been used for this time interval between the touching of the keel and that of the boat axis to give a linear increase of the acceleration. Now, substituting all these forces computed so far into Equations (10)- (12), the horizontal, vertical and rotational motion of the boat in global coordinate system can be computed. However, an occupant on a

5 Water free-fall lifeboat local coordinate will experience system. have been transformed according the relationships and the normal Calculated Experimental During and system : (34) (35) for the occupants directions results in accelerations into the local coordinate where a# and ac are the accelerations 4. Simulation accelerations So the computed to the following in the axial Entry of the boat. comparison with data the water entry the water water (see Fig. 4). ed by the authors stern) of a free-fall lifeboat there and the entry of the stern into the Model experiment has been conductto verify the numerical model also shows these phenomena. In this chapter these phenomena by comparing the we will discuss computed and Lifeboat in local 197 coordinate system as shown in Fig. 3. Numerical simulation has also been carried out for the same model. The results of numerical simulation as calculated in Equations (34)-(35) and model mental data are shown in Fig. 5 to Fig. 8. Fig. 5 compares tions three the computed and measured experiaccelera- in the normal direction to the axis of the boat at positions 167 mm, 500 mm and 833 mm from the aft end of the boat. The boat θ = 30, fall H tance are two distinct events that produce significant accelerations on the boat. These events are the impact of the bow with of Free-Fall from height, the lowest = 1.40 fell at an initial m and slidlng end of the skid angle of length (dis- to the centre of gravity of the boat at the instant of falling start), Lgo, =0.80 m. The results of numerical simulation have been shown on the left and the measured data on the right part of this figure. It is seen from Fig. 5 that at the bow position the peak acceleration in the normal tion caused by bow impact with the maximum about 4.2 g are obtained from both numerical direcvalue of simula- tion and experiment. It is also shown that the stern impact occurs after the bow impact and the magnitude measured results. The model test has been performed using the lifeboat of the acceleration model angle keeping stern impact computed happens a little faster than model experiment. This is because the still water of Table 1 for different falling the falling height constant. Accelerations in normal direction to the boat axis and along the boat axis have been measured in three positions (near bow, midship and becomes surface has been assumed bow impact in the numerical comparatively undisturbed computation. large. The even after the On the other hand, as shown in Fig. 4, a large deformation of free surface will occur in the model experiment due to the impact of the bow and it affects the stern impact. There are fluctuations in the experimental which are caused by a local vibration of especially lifeboat. at the stern Fig. 6 compares tions Table Fig. 4 Water entry (θ = 30, H of the lifeboat = 1.4 m, Lg0'= in experiment 0.8 m) in axial 1 part during the computed direction stern the impact results body of the and measured accelera- of the boat at different positions Principal dimensions of the lifeboat used in experiment and simulation model

6 198 Journal of The Society of Naval Architects of Japan, Vol. 178 Fig.5Normal acceleration in different positions (0=30, H=1.40 m, Lg0'=0.80 m) (positive : upward acceleration) Fig.6Axial acceleration in different positions (e=30, H=1.40 m, Lg0'=0.80 m) (positive: forward acceleration) Fig.7Normal acceleration in different positions (O 40, H=-1.40 m, Lg0'=0.29 m) (positive : upward acceleration)

7 Water Entry Simulation of Free-Fall Lifeboat 199 for the same case as was shown in Fig. 5. The peak decelerations by numerical simulation are almost 3.1 g in three positions and almost the same values were obtained by the model experiment. Fig. 7 shows the accelerations in normal directions obtained by numerical simulation and by experiment for three positions of the boat. The boat has been released at a falling angle O4, at a falling height H =1.4 m and sliding length Lg0'=0.29 m. The peak normal acceleration for bow impact at the bow position is about 3.2 g by the numerical simulation and almost the same value was measured in the model experiment. The maximum acceleration at the stern occurs when the aft part of the boat enters the water surface. Fig. 8 presents the acceleration in axial direction. The magnitude of the maximum decelerations and the patterns of acceleration histories are almost the same for three different positions. Fig. 9 shows the calculated trajectory of the axis of the free-fall lifeboat model (longitudinal line through the center of gravity of the boat, see Fig. 2) falling at an initial angle 0=30 and from a height H=1.40 m. At first, the boat slides along the skid of length 1.4 m with a sliding length Loy = m. Then it rotates clockwise direction and falls freely until it touches the water surface. After it touches the water surface, impact Fig.8Axial acceleration in different positions (e=40, H=1.40 m, Lg0'=0.29 m) (positive : forward acceleration) Fig.9Simulated trajectory of lifeboat model (0=30, H=1.40 m, Lg0'=0.80 m)

8 200 Journal of The Society of Naval Architects of Japan, Vol. 178 Fig.10Simulated trajectory of lifeboat model (0= 40, H=1.40 m, =0.29 m) force due to the change in added mass and buoyancy force start to act. Buoyancy force is increasing as long as the boat goes into water until it reaches to its maximum immersion (almost 0.25 m). During this time, the boat starts rotating in the opposite direction (i. e., anti-clock wise) due to the buoyancy moment and the moment due to momentum transfer. At that time the axis of the lifeboat disappears fully inside water and a large buoyancy force pushes it up. The boat then comes out of the water and falls down again into water with already forwarding some distance. This process continues till the boat stops. This falling and traveling process of the boat has been confirmed by the video tape recorded during the experiment. Fig. 10 shows the calculated trajectory of the axis of the free-fall lifeboat model falling at an initial angle 0 =40 and from a height H=1.40 m. The boat slides along the skid of length 1.4 m with sliding length L90'= 0.29 m. The falling process of this 0=40 case is similar to the previous case though the center of gravity travels in different path. It is seen from Fig. 10 that the advance speed in the water is very slow as compared to 0=30 falling case. Especially during the water exit process, the trajectory of the center of gravity of the boat becomes almost vertical and the boat rises up quickly in the air before it falls down again. The boat does not move forward so much and remains almost in the same position with some oscillations. 5. Conclusions A mathematical model has been presented in this paper which can be used to predict the launch behaviour of skid-launching free-fall lifeboats. The boat has been treated as a rigid body when equations of motion for the four falling phases of the lifeboat was numerically solved. The behaviour of the lifeboat has been studied for different impact conditions both numerically and experimentally. From the above study the following remarks have been shown to be important. 1. Free-fall lifeboat experiences two distinct impacts during its launching. They are impact of the bow with the water and the entry or impact of the stern into the water. 2. Bow impact causes maximum acceleration at the bow and stern impact causes maximum acceleration at the stern in normal direction. 3. The bow impact has more influence than stern impact in axial direction at any positions of the boat. 4. Due to the deformation of the water surface, the timing of the stern impact experienced by the boat actually is later than obtained by the numerical simula- tion. 5. Impact has maximum influence on acceleration during water entry but buoyancy and drag control the motion after full entry of the boat. 6. The present numerical method effectively predicts the magnitude and direction of the accelerations in different positions of a free-fall lifeboat. It can also be used to evaluate the motions of the boat for different falling conditions. Acknowledgement The authors would like to express their gratitude to Dr. R. Tasaki and Dr. A. Ogawa for their helpful discussions regarding this study. The authors also like to thank Dr. S. Yamashita, Ishikawajima Harima Heavy

9 Water Entry Simulation of Free-Fall Lifeboat 201 Industries, Co., Ltd, for the cooperation in model experiment. This research was partially supported by the Sasakawa Scientific Research Grant from The Japan Science Society. References 1) von Karman, T.: The Impact on Seaplane Floats during Landing, NACA TN 321, (1929). 2) Werenskiold, P.: Design of Free-fall Lifeboat System, International Conference on Marine Survival Craft, London, (1983). 3) Tasaki, R., Ogawa, A., and Tsukino, Y.: Numerical Simulation and Its Application on the Falling Motion of Free-Fall Lifeboats, Journal of The Society of Naval Architects of Japan, Vol. 167 (1990). 4) Nelson, J. K., Fallon, D. J. and Hirsch, T. J. : Mathematical modelling of Free-Fall Lifeboat Launch Behavior, OMAE-Volume I-B, (1991). 5) Boef, W. J. C.: Launch and Impact of Free Fall Lifeboat (Part I and Part II), Ocean Engineering, Vol. 19, (1992). 6) Arai, M. and Khondoker, M. R. H.: Motion Simulation of Falling Bodies During Water Entry : Basic Study With Cylinders, Journal of The Kansai Society of Naval Architects of Japan, Vol. 222 (1994). 7) Hoerner, S. F.: Fluid Dynamic Drag, New Jersey, U. S. A., (1958). 8) Y. Yamamoto, M. Fujino, and T. Fukasawa : Motion and Longitudinal Strength of a Ship in Head Sea and the Effects of Non-Linearities (First Report), Journal of The Society of Naval Architects of Japan, Vol. 143 (1978).