Hydrodynamic impulse generated by slender bodies undergoing unsteady motion in viscous flows. (15th September 2021) - Doyle, R.; Jeans, T.L.; Holloway, A.G.L.
Abstract: The forces and moments on a UUV hull undergoing unsteady sway motions are analyzed using both traditional methods which integrate the pressure and shear stress at the wall, and hydrodynamic impulse based methods which analyze the vortical structure of the flow around the body. Computational fluid dynamics simulations have been conducted of a body with a slenderness ratio of 8.5, at a Reynolds number of 3.4 million, undergoing a variety of sway maneuvers. These include steady translations at incidence angles from 0 ∘ to 20 ∘, impulsive acceleration with varied initial incidence, and sinusoidally oscillating sway over a range of frequencies and amplitudes. The impulse based method is based on a body-fixed, non-inertial frame used to analyze the vortical structures near the body. It is demonstrated that this impulse based analysis provides a sensible decomposition of unsteady forces into those due to added mass and those due to unsteady circulation and motion history. Motion history effects are seen to be primarily described by the Lamb vector distribution around the body. These effects decay towards the quasi-steady limit at large times for impulsive motion and at low frequencies for sinusoidal motion. This is demonstrated with the analysis of the impulse based force components and with visualizations of the vortex structures in the flow field. A simplified form of the impulse based equations is derived and validated, based on approximations from slender body theory. Highlights: An unsteady formulation of the hydrodynamic impulse method is described. The method is applied to a slender axisymmetric body during unsteady translation. Impulse method results compare well to the integrated pressure and shear stress. The impulse method is shown to split forces into added mass and circulatory terms. A simplified form of the impulse method is derived using slender body theory.