Free Oscillations of a Liquid during Spin-up,
Abstract
Eigenfrequencies of a liquid in a fully-filled circular cylinder during spin-up are shown to be always real (hence the flow is stable), provided that there is no singularity (critical layer) in the flow. For rotationally symmetric disturbances the liquid eigenfrequencies at several successive instants during the phase of spin-up are determined. The conditions for the existence, the location, as well as the nature of the singularity based on an inviscid formulation are demonstrated. Regular and singular solutions of the inviscid system having a critical layer in the flow, are obtained in series form. The exact viscous system governing amplitudes of arbitrary disturbances is reduced to two coupled equations in two dependent variables. A differential equation governing approximately the viscous disturbances in the vicinity of a singularity is obtained. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1973
- Accession Number
- AD0769710
Entities
People
- Y. M. Lynn
Organizations
- Ballistic Research Laboratory