Numerical model of a marine chute evacuation system
Introduction
The marine evacuation chute is one of the methods of providing a means of escape during an emergency situation on a ship or offshore oil installation. It is a gravity launch system that enables efficient evacuation of personnel in a relatively short time. The safety of these systems are usually evaluated under calm conditions and it is important to assess their behaviour under extreme environmental conditions. We present a numerical model for the purpose of quantifying the dynamic behaviour (motions and tensions) of a typical marine evacuation chute under wind loading, internal mass flow and prescribed motions of both ends. A lumped-mass model is used and the equations are formulated using Kane's method (Kane and Levinson, 1985). The simulation results will be useful for designing chutes for extreme weather conditions.
Section snippets
System configuration
A sketch of the system to be analysed is given in Fig. 1 and a lumped mass model is illustrated in Fig. 2. The origin of inertial coordinates is an arbitrary point O and the unit vectors of the inertial frame are denoted by . The chute is divided into segments by points . The mass of each segment is lumped in halves at the ends except for segments and , the masses of which are lumped at points and , respectively. The n lumped masses at points
Inertia forces
The generalized inertia force isThis may be written in matrix form aswhere is the column vector of values and is a diagonal matrix defined as
Gravity
The net force on lumped mass due to gravity . The generalized active force due to gravity is
Tension
The stiffness of segment of the chute is defined in the usual way as where are, respectively, the material area of cross-section, modulus of elasticity and unstretched length of the segment. The instantaneous length of the segment is denoted by (Eq. (2.7)). We allow for tension but not for compression. To this end, we define the elongation of segment aswhich is identically zero if the instantaneous segment length becomes
Structural damping
In any line segment, the damping force on the end masses is of the form , where is the velocity of one mass relative to the other, is the unit tangent vector along the segment and is a structural damping coefficient. The force on particle due to structural damping in segment may be written in the formwhereand is the damping coefficient for segment . The generalized active force due to structural damping in segment
Wind load
Consider segment , diameter , unstretched length . Assume that the segment has a velocity equal to the velocity of its mid-point and is given byThe velocity of the wind relative to iswhere is the wind velocity. Let the unit vector normal to in the plane defined by and be and let the components of in the and directions be and , respectively (Fig. 3). ThenLet , be
Internal mass transport
We assume that the steady transport of people down the chute in an evacuation process may be approximated by the flow of a fluid of density given bywhere is the total mass inside the chute at steady flow and is the internal volume of the chute. To determine the force on the chute at point we consider the control volume ABCD illustrated in Fig. 4. For , the control volume consists of the second half of segment and the first half of segment . For , it
Guide wires and counterweight
Some marine chute systems are designed with a sub-surface counterweight attached to guide wires running along the outside of the chute. The wires and the counterweight are not supported by the chute material itself and their purpose is to keep the chute straight. If the net guide wire tension is , the forces exerted on the chute lumped masses arewhere is the unit vector from to the counterweight. We note that point is attached to a moving
Equations of motion
To write the equations of motion, we assemble the components of the generalized inertia and active forces. Matrices will be denoted by square brackets and column vectors by curly brackets. The total generalized inertia force iswhere, from Eqs. (3.2), (8.15)The total generalized active force for the system isWe are now able to write the system of coupled nonlinear equations of motion (Kane
Results
For evacuation from a typical offshore oil vessel (FPSO), we consider a chute of length 32 m, internal diameter 1.2 m constructed of synthetic material. The weight-bearing characteristics are provided by four 20 mm Kevlar ropes running lengthwise through the fabric. In order to test the algorithm, two special cases were considered for which analytic results are available. The first case consisted of fixing the end points at known positions and allowing the structure to respond under
Conclusions
A procedure for simulating the three-dimensional dynamic behaviour of marine evacuation chute systems has been presented using the techniques outlined by Kane and Levinson (1985). The chute is considered to be a flexible tube with internal mass transport and with prescribed motions at the ends. It is common to test such systems in benign conditions and it is therefore desirable to have a tool such as the algorithm presented here for assessing their reliability and predicting their behaviour in
Acknowledgements
The authors would like to thank James Boone (Marine Institute, Memorial University of Newfoundland) for supplying data for the chute. The diagram in Fig. 1 was provided by Tom Hall (Institute for Ocean Technology). Funding was provided by the Program for Energy Research and Development (Government of Canada).
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