Hysteretic configurations in a rotating U-tube with capped ends

作者：Weidman P D^*

来源：Fluid Dynamics Research, 2015, 47(3): 035501.

DOI：10.1088/0169-5983/47/3/035501

• U-tube
• rotation
• capped ends
• hysteretic response

The effect of air trapped above the liquid columns in a U-tube rotating about an axis offset from the axis of symmetry is investigated. This extends the work of Denardo, Barber, Folley and Wright (Am. J. Phys., 57, 1989) who investigated the same problem for an open-ended U-tube for which no air is trapped. They found that, owing to a combination of gravitational, centrifugal and constraint forces on the liquid, the position of the liquid-air interfaces can be hysteretic as the angular velocity is varied. The existence and strength of the hysteresis loop depends on the dimensionless offset parameter d and the dimensionless initial liquid height gamma. Associated with the hysteresis is an instability in which the liquid jumps from one equilibrium state to another, herein defined as configuration I and configuration II. With the ends of the U-tube capped, the stable liquid configurations depend on two additional parameters defined for a stationary U-tube: alpha, the initial ratio of trapped air to liquid volume in each U-tube column and beta, the normalized pressure of air trapped above the liquid in each column. In this study beta is taken at the constant value corresponding to atmospheric pressure and, based on a previous study, we adopt Boyle's law for determining the expansion/compression of air in a rotating U-tube. A parametric study varying alpha shows that a critical value occurs marking the threshold between hysteretic and nonhysteretic states. A parametric study of the effect of delta is also presented.

• 出版日期2015-6