Contribution of Pressure to The Moment during Spin-Up on a Nutating Liquid-Filled Cylinder: Ad Hoc Model
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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A study is made of the flow of a liquid in a cylindrical container that nutiates at constant frequency and small amplitude and impulsively begins spinning with a fixed angular velocity. In particular, the history of pressure overturning moment during spin-up is investigated. The partial differential equations of the problem are linearized, and a modal analysis separated variable solution is applied. One consequence of stipulating a modal analysis is a difficulty with endwall boundary conditions this difficulty is avoided here by specifying a heuristic boundary condition and then satisfying it approximately. Calculations indicate that peaks of overturning or restoring moment occur at or near those times when the nutational frequency is equal to one of the frequencies of inertial oscillations of the liquid. This phenomenon of resonance extends the result of Stewartson obtained for inviscid perturbations in solid body rotation.
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