Elsevier

Ocean Engineering

Volume 34, Issues 5–6, April 2007, Pages 739-746
Ocean Engineering

Numerical model of a marine chute evacuation system

https://doi.org/10.1016/j.oceaneng.2006.05.002Get rights and content

Abstract

A lumped-mass model of a marine evacuation chute is presented based on the equations of Kane. The effects of wind load, internal mass transport and the motions of the ends are included. A sample of predicted motions and tensions is presented for a typical extreme environmental condition. The model may be used to assess the behaviour of the chute structure under a variety of emergency evacuation scenarios.

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 N1,N2,N3. The chute is divided into n+1 segments Sk(k=1,,n+1) by points P0,P1,,Pn+1. The mass of each segment is lumped in halves at the ends except for segments S1 and Sn+1, the masses of which are lumped at points P1 and Pn, respectively. The n lumped masses at points P1,

Inertia forces

The generalized inertia force isFr*=j=1nvrPj·(-mjPjaPj)(r=1,,3n).This may be written in matrix form as{F*}=-[V]{u·},where {u·} is the 3n×1 column vector of ur· values and [V] is a 3n×3n diagonal matrix defined asV3j-2,3j-2=V3j-1,3j-1=V3j,3j=mj(j=1,,n).

Gravity

The net force on lumped mass mj due to gravity -mjgN3. The generalized active force due to gravity isFrG=j=1n-mjgN3·vrPj.

Tension

The stiffness kSj of segment Sj of the chute is defined in the usual way as kSj=A0Elj,where A0,E,lj 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 Z4,j (Eq. (2.7)). We allow for tension but not for compression. To this end, we define the elongation of segment Sj asZ5,j=12[(Z4,j-lj)+|Z4,j-lj|](j=1,,n+1)which 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 ±Cs(vR·t)t, where vR is the velocity of one mass relative to the other, t is the unit tangent vector along the segment and Cs is a structural damping coefficient. The force on particle Pk due to structural damping in segment Sk may be written in the formDPk=gktk(k=1,,n),wheregk=-CSk(vPk-vPk-1)·tksign(Z5,k)and CSk is the damping coefficient for segment Sk. The generalized active force due to structural damping in segment Sk

Wind load

Consider segment Sk, diameter dk, unstretched length k(k=1,,n+1). Assume that the segment Sk has a velocity equal to the velocity of its mid-point and is given byVSk=12(vPk+vPk-1)(k=1,,n+1).The velocity of the wind relative to Sk isvRk=UW-VSk,where UW is the wind velocity. Let the unit vector normal to tk in the plane defined by tk and vRk be nk and let the components of vRk in the tk and nk directions be vtk and vnk, respectively (Fig. 3). Thenvtk=(vRk·tk)tkandvnk=vRk-vtk.Let CDTk, CDNk 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 ρ˜ given byρ˜=MTVc,where MT is the total mass inside the chute at steady flow and Vc is the internal volume of the chute. To determine the force on the chute at point Pk we consider the control volume ABCD illustrated in Fig. 4. For k=2,,n-1, the control volume consists of the second half of segment Sk and the first half of segment Sk+1. For k=1, 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 Tw, the forces exerted on the chute lumped masses areFPk/wire=Tw(tk+1-tk)k=1,,n-1,Tw(nc-tn)k=n,where nc is the unit vector from Pn to the counterweight. We note that point Pn+1 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 is{F*}total={F*}+{F˜*}=-[A]{u·},where, from Eqs. (3.2), (8.15)[A]=[V]+[V˜].The total generalized active force for the system is{F}total={FG}+{FT}+{FSD}+{FD}+{FL}+{F˜}+{F˜G}+{Fwire}.We are now able to write the system of 2m(m=3n) 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 (E=131GPa) 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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