95/05364 Nitrate in groundwaters of the Central Valley, Costa Rica

Abstract

In this study it is shown that the transition from the homogeneous to the heterogeneous flow regime in bubble columns can be quantitatively found with high accuracy by analysing the chaotic characteristics of the pressure fluctuation signal (PFS). In previous work (van den Bleek and Schouten, 1993; Schouten et al., 1996), the authors have already applied this technique to time series from gas-solid fluid beds. Also, it was shown (Krishna et al., 1993, Ellenberger and Krishna, 1994) that hydrodynamics of bubble columns and fluid beds can be described in an analogous manner. Therefore in this work, the method of chaos analysis is applied to bubble columns. A distinctive feature of the pressure signal from bubble columns is that it is composed of two different parts: a low frequency part resulting from the motion of the large bubbles and a high frequency part resulting from all other processes (coalescence, collapse, breakup) that take place in the column. From the phase of the cross spectrum of two pressure probes, placed at different axial positions, it was possible to identify the bands in the spectrum of the PFS that show a significant time delay. This time delay is of the order of the passage time of bubbles between the measurement locations. This band in the spectrum of the PFS was used to estimate the Kolmogorov entropy to quantify the chaotic dynamics in the bubble column. The Kolmogorov entropy as a function of gas velocity indicates a sharp transition from the homogeneous to the churn-turbulent flow regime. From other methods considered (e.g. holdup and other properties of the signal such as variance), this transition was less clear. Therefore chaos analysis of PFSs is believed to be a powerful technique for on-line identification of flow regimes.