The Onset Of Resonance In Two-Immiscible Fluids Inside A Spinning And Coning Cylinder

Abstract

Resonance of the motion of two fluids inside a cylinder that spins about its axis and rotates (cones) about an axis that passes through its center of mass is known to occur for low-viscosity fluids (high Reynolds number flows) at critical geometric parameters and coning frequencies. In this paper the motion of two inviscid fluids inside a spinning and coning cylinder is analyzed by the method of separation of variables for small coning frequencies and/or coning angles. The analytical solution of the inviscid flow equations provides a criterion in the form of a transcendental equation that governs the behavior of the parameters that cause resonance. The transcendental equation was solved numerically by Newton-Raphson's iteration and the results are in good agreement with those obtained for two viscous fluids.