Unsteady Rotating Flow in a Cylinder With a Free Surface

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.

Observations of vortex breakdown in an open cylindrical container with a rotating bottom

“…Goller and Ranov, 1968). Published results mainly deal with the transient flow in open cylindrical containers, which rotate about their axis of symmetry (e.g.…”

A primitive variable, strongly implicit calculation procedure for two and three-dimensional unsteady viscous flows: applications to compressible and incompressible flows including flows with free surfaces

“…It was observed from a literature review that liquid sloshing problems have generally been restricted to either cylindrical [42] or rectangular [39] geometries.…”

Viscous Effects in the Wedemeyer Model of Spin-up from Rest

“…However, it also satisfi'es (14) in Reference 4, in slope and curvature, when the core flow is almost solid-body rotation.…”