Vehicle Motion in Currents

Abstract

In this paper, we present a nonlinear dynamic model for the motion of a rigid vehicle in a dense fluid flow that comprises a steady, nonuniform component and an unsteady, uniform component. In developing the basic equations, the nonuniform flow is assumed to be inviscid, but containing initial vorticity; further rotational flow effects may then be incorporated by modifying the angular rate used in the viscous force and moment model. The equations capture important flow-related forces and moments that are absent in simpler models. The dynamic equations are presented in terms of both the vehicle's inertial motion and its flow-relative motion. Model predictions are compared with exact analytical solutions for simple flows. Applications of the motion model include controller and observer design, stability analysis, and simulation of nonlinear vehicle dynamics in nonuniform flows. As illustrations, we use the model to analyze the motion of a cylinder in a plane laminar jet, a spherical Lagrangian drifter, and a slender underwater vehicle. For this last example, we compare predictions of the given model with those of simpler models and we demonstrate its use for flow gradient estimation. The results are applicable to not only underwater vehicles, but also to air vehicles of low relative density such as airships and ultralights.