Abstract
Abstract Due to the complex flow structure and non-uniform phase distribution in the vertical upward gas-liquid two-phase flow, an eight-electrode rotating electric field conductance sensor is used to obtain multi-channel conductance signals. The flow patterns of the vertical upward gas-liquid two-phase flow are classified according to the images obtained from a high-speed camera. Then, we employ the multivariate weighted multi-scale permutation entropy (MWMPE) to detect the instability of flow pattern transition in the gas-liquid two-phase flow. Afterwards, we compare the results of the MWMPE with those of the single-channel weighted multi-scale permutation entropy (SCWMPE) and multivariate multi-scale sample entropy (MMSE). The comparison results indicate that, compared with the SCWMPE and MMSE, the MWMPE has superior performance in terms of the high-resolution presentation of flow instability in the gas-liquid two-phase flow. Finally, we extract the mean value of the MWMPE in whole scales and the entropy rate of the MWMPE in the small scales. The results indicate that the normalized mean value and normalized entropy rate of MWMPE are very sensitive to the transitions of flow patterns, thus allowing the detection of the instability of flow pattern transition.
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