Efficient numerical schemes were presented for the steady state solutions of towed marine cables. For most of towed systems, the steady state problem can be resolved into two-point boundary-value problem, or initial value problem in some special cases where the initial values are available directly. A new technique was proposed and attempted to solve the two-point boundary-value problem rather than the conventional shooting method due to its algorithm complexity and low efficiency. First, the boundary conditions are transformed into a set of nonlinear governing equations about the initial values, then bisection method is employed to solve these nonlinear equations with the aid of 4th order Runge-Kutta method. In common sense, non-uniform (sheared) current is assumed, which varies in magnitude and direction with depth. The schemes are validated through the DE Zoysa's example, then several numerical examples are also presented to illustrate the numerical schemes.
A numerical method is developed to investigate the dynamic response of cable-seabed interaction in this paper. The motion of cable is described by the Lumped Parameter Method, while the seabed, unlike the prevailing simplified model of elastic foundation, is modeled as an irregular continuous rigid surface with rebound and friction existing, and the forces exerted by the seabed consist of normal counterforce and isotropic tangential Coulomb friction resistance. To describe the detailed dynamic response, two coefficients are introduced by analogy with the theory of rigid body collision with friction. The cable-seabed kinematic and dynamic contact conditions are formulated subsequently, and are used to incorporate the seabed effect into the cable dynamics to produce a set of ordinary differential governing equations. In this paper, we employ 4th order Runge-Kutta method to solve these equations. Several simulation cases are presented to illustrate the seabed effect. The results show that friction and impact have a prominent influence on the statics and dynamics of the cable.
The parallel processing based on the free running model test was adopted to predict the interaction force coefficients (flow straightening coefficient and wake fraction) of ship maneuvering. And the multipopulation genetic algorithm (MPGA) based on real coding that can contemporarily process the data of free running model and simulation of ship maneuvering was applied to solve the problem. Accordingly the optimal individual was obtained using the method of genetic algorithm. The parallel processing of multi-population solved the prematurity in the identification for single population, meanwhile, the parallel processing of the data of ship maneuvering (turning motion and zigzag motion) is an attempt to solve the coefficient drift problem. In order to validate the method, the interaction force coefficients were verified by the procedure and these coefficients measured were compared with those ones identified. The maximum error is less than 5%, and the identification is an effective method.
It is very difficult, for the component-type ship mathematical model, to estimate the interaction force coefficients among the hull, propeller and rudder. Some coefficients such as wake fraction and flow straightening coefficient were studied from the model tests in different loading conditions and the normal force of rudder was tested in captive model tests to obtain the coefficients. From these results of the tests, the flow straightening coefficients increase with the increase of trims or drafts. Similarly, wake fraction coefficients are larger for the large drafts, however, become small as the trims increase. The resistance is obviously different in fully loaded condition with the trims by stern, however , the difference is not evident when the draft decreases and the bulbous bow is above the water surface.
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