Diagnosis of chaotic dynamics of bubble motion in a bubble column

Abstract

The motion of bubbles in a two-dimensional bubble column was characterized by the deterministic chaos analysis of time-series data of bubble frequency, measured locally by an optical transmittance probe with a narrowed HeNe laser beam. To diagnose the dynamics of bubble motion, three different methods were applied to the series of time intervals between two successive bubble passages: (i) the correlation dimensions were estimated from the reconstructed attractors, (ii) using the short-term predictability analysis, the deterministic and random features in the bubble motion were characterized in terms of Mann-Whitney statistic, and (iii) the value of the Hurst exponent was computed using the rescaled range (R/S) analysis. All three parameters were found to show consistent and significant changes at the transition between homogeneous bubble flow and heterogeneous churn-turbulent flow. These results indicate that at low velocity the motion of bubbles in the bubble column is deterministic chaotic whereas at high gas velocity the random-like motion of bubbles becomes significant.