Evaluation of the effect of secondary flows on the oscillations of an oscillating-cup viscometer

The behavior of damped torsional oscillations of a cylinder filled with a Newtonian incompressible fluid with respect to the axial and radical components of its velocity was discussed. It was assumed that there was no slip between the fluid and the inner surface of the cylinder. The flow was assumed to be axisymmetric, the damping of the oscillations in the absence of the fluid to be negligibly small, and the fluid wetted both end walls of the cylinder. The calculation was performed using the finite difference technique such as the semi-implicit method of variable directions with the time derivatives approximated by the three layer scheme or the Crank-Nicolson. Thus, to eliminate the effects of secondary flows and allow using the conventional calculation formulas, experiments must be carried out in the region of low viscous approximation with crucibles whose height is not less than the radius.