Virtual Planar Motion Mechanism Testing of 8:1 Spheroids

Abstract

PMM testing is a method used to identify the added mass and damping coefficients used in the equations of motion of a vehicle by attempting to decouple the forces on a body due to velocity and acceleration as a result of creating "hydrodynamically pure" velocities and accelerations. This makes it possible to use quasi-steady state models with terms independent of both velocity and acceleration. This paper explores the ability of simple damping models (solely a function of velocity) with added mass terms (solely a function of acceleration) to simulate the heave force of an 8:1 ellipsoid undergoing PMM testing. In order to help explain the complexity of the flow during PMM tests, a flow analysis of the 8:1 spheroid is provided, which discusses the flow topology of spheroids at steady angle of attack, validity of quasi-steady models, and some other basic flow features seen in PMM testing. In this paper, a simple proportionality relationship between a linear and quadratic damping model is revealed. It is also shown that variations in the heave force response during PMM tests are most heavily influenced by viscous effects, especially cross flow separation. Finally, it is shown where these models break down, owing to the increasing nonlinearity of the flow induced by the harsher motions of large amplitude and/or large frequency tests.