Theoretical Analysis of Experimentally Observed Perplexing Calibration Characteristics of Ball-in-Vortex Flow-Meter

Abstract

This investigation analyzes the calibration nonlinearity of the ball-in-vortex flow-meter, designed to work on the principle of a rotating sphere in and due to a vortex flow. The comparison of this flow-meter reading with the standard flow-meter indicates the existence of different calibration regimes, bifurcated by a sharp change in slope of the calibration curve. Based on the governing mechanics of this flow-meter, this paper explains this nonlinearity, and proposes its mathematical form. In particular, the bifurcation in calibration characteristics is attributed to the change in the surface contact frictional force, due to translation of the ball. The mathematical model captures the various calibration regimes associated with this translation, from one plane of rotation in the flow-meter to another, or from one periphery to another. Thus, calibration nonlinearity of this flow-meter can be fully comprehended through its governing mechanics, and harnessed for flow measurement.