Unsteady Rotating Flow in a Cylinder With a Free Surface

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Abstract
The investigation deals with the “spin-up” of the liquid partially filling a right circular cylinder which is impulsively accelerated from rest to a constant angular velocity. By application of certain simplifying assumptions, a simplification of the Navier-Stokes equations is obtained and numerically solved, obtaining the unsteady angular velocity distribution of the liquid and the configuration of the liquid’s free surface, as it approaches, asymptotically with time, a paraboloid. The simplifying assumptions are qualitatively verified by experiment. Measurement of the theoretically predicted free-surface configuration is obtained by an electrohydraulic servosystem designed and developed for the problem. Good agreement between experiment and theory is obtained.

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