A comparison between mathematical models of stationary configuration of an undewater towed system with experimental validation

The analysis of underwater towed systems attracted the interest of many researchers because of the recent years utilization of remotely-operated underwater vehicle (ROV) and towed array in offshore and military applications. The purpose of this work is to show, by experimental validation, that towed cable configurations may be computed effectively and accurately by discretizing the towing cable rather than using a continuous modeling approach. Two mathematical models have been developed to predict the stationary configuration of an underwater towed system loaded by hydrodynamic forces. The system is composed of a towed inextensible cable, with no bending stiffness, and a depressor that is fixed at the cable free end. This configuration is currently used for underwater remotely-operated vehicle. This work investigates the comparison between continuous and discrete models of the 2D static equations of the steady-state towing problem in a vertical plane at different towing speeds. The results of the models have been validating using experimental trials. In the first part of this paper, a continuous model is presented, which is based on geometric compatibility relations, equilibrium equation. A set of nonlinear differential equations has been derived and solved using Runge-Kutta iterative procedure. In the second part, a discrete rod model is proposed to determinate the cable shape, which is based on a system of nonlinear algebraic equations that are solved numerically. This two models are both suitable for analyzing an underwater towed system having a known top tension and inclination angle obtained from experiments. The third part of the paper describes the experiments, which have been in a towing tank basin (CNR-INSEAN). In the fourth and last part of this study it is demonstrated the effort and cost of numerically integrating the continuous model do not compare favorably with the relative ease and efficiency of solving the discrete model, which yields the same results.