Liquid moment on a filled coning cylinder during spin-up: Ad hoc model

A liquid-filled right circular cylinder, coning at constant frequency and small amplitude, impulsively begins spinning with a fixed angular velocity. The ensuing history of the moment, i.e., pressure plus viscous shear, exerted by the liquid on the container is investigated here by computation of the quasi-steady state response of the fluid to the motion of the shell. The partial differential equations of flow are linearized, and a modal analysis (separated variable solution) is applied. The difficulty with endwall boundary conditions which arises from stipulating a modal analysis is avoided by specifying a heuristic boundary condition and then satisfying it aproximately. The current procedure for approximating the boundary condition is an improvement over the one employed in previous work (ARBRL-TR-02563) to obtain the pressure moment. Calculations indicate that peaks of overturning moment occur at or near those times when the coning frequency is equal to one of the frequencies of inertial oscillations of the liquid. This phenomenon of resonance extends the results of Stewartson obtained for inviscid perturbations in solid body rotation. Included here also are a discussion of the accuracy of a part of the method and comparisons with output of the inviscid perturbation method and the above-mentioned previous method.