An impulse framework for hydrodynamic force analysis : fish propulsion, water entry of spheres, and marine propellers

Abstract

This thesis presents an impulse framework for analyzing the hydrodynamic forces on bodies in flow. This general theoretical framework is widely applicable, and it is used to address the hydrodynamics of fish propulsion, water entry of spheres, and the offdesign performance of marine propellers. These seemingly-unrelated physics problems share a key common thread: The forces on these fish, spheres, and propellers can be modeled as the sum of the reaction to the rate of change of (1) the pressure impulse required to set up the potential flow about the body, and (2) the vortex impulse required to create the vortical structures in the wake of the body. Fish generate propulsive forces by creating and manipulating large-scale vortical structures using their body and tail. High-speed particle image velocimetry experiments show that a fish generates two vortex rings during a C-turn maneuver and that the change in momentum of the fish balances the change in pressure impulse plus the vortex impulse of these rings. When a sphere plunges into a basin of water and creates a sub-surface air cavity in place of a vortical wake, the vortex impulse is zero, and the force on the sphere is given by the pressure impulse component. Using data from high-speed imaging experiments, a semi-empirical numerical simulation is developed herein; this numerical model shows how the presence of the cavity alters the unsteady pressure force on the sphere and modulates the dynamics of the impact event. During steady propeller operation, the pressure impulse is constant, and the loads on the propeller are given by the vortex impulse component. To analyze these loads, a computational design and analysis tool is presented; this code suite is based on propeller lifting line theory, which is shown to be a special case of the general impulse framework of this thesis. A marine propeller is designed, built, and tested over a range of off-design operating conditions. Experimental results match the predicted performance curve for this propeller, which provides important validation data for the numerical method presented herein. 3 Bringing this thesis full circle, the unsteady startup of the propellor is addressed, which is analogous to the impulsive maneuvering of the swimming fish. As in the fish maneuvering problem, the propellor generates a ring-like vortical wake, and it is shown herein how the vortex impulse of these rings provides thrust for the propellor. With the perspective of the impulse framework developed in this thesis, the results of these tandem experimental investigations and numerical simulations provide deeper insight into classical fluid-dynamics theory and modern experimental hydrodynamics.