Surrogate testing for nonlinear hydrodynamics in bubble columns

Surrogate testing is often used to examine the possible deterministic nature of time series at the first step. In this study, the method of surrogate testing was applied to hydrodynamic time series in bubble columns. The hydrodynamic time series were measured in three gas-liquid systems bubble columns, with inner diameters of 20, 40, and 80 cm. The gas velocity varied from U-g = 3.3 cm/s to U-g = 9.0 cm/s. The determinism of these hydrodynamic time series was examined in terms of three methods of surrogate testing: local flow, local dispersion, and nonlinear prediction. Three types of surrogate data algorithmsFourier-shuffled, phase-randomized, and Gaussian-scaledserved as stochastic controls. Therefore, a total of nine sets of tests were conducted for each experimental time series. If any of these surrogate data exhibits a similar distribution with the original time series, the hypothesis that the hydrodynamic time series in bubble column is generated with linear stochastic process is assumed not to be able to be rejected. Two samples were given in detail to show how to implement the calculation. Measurements for one experimental time series were obtained from the 80-cm bubble column with U-g = 3.3 cm/s; eight of the nine tests indicated that the original time series was not linear-stochastic. Results for another experimental time series were obtained from the 20-cm bubble column, with U-g = 9.0 cm/s; five of the nine tests indicated that the original time series was not linear-stochastic, and four of the nine show that the null hypothesis was assumed not to be able to be rejected at a 99% level of significance. Such test results indicates that the dynamic nature of hydrodynamics in bubble columns may be rather complex and may contain a stochastic component. The strength of the stochastic component is dependent on the flow conditions in the bubble columns.