In this paper, we first extract a nonlinear time series from the Welerestrass function as a toy model and investigate the anti-noise ability of six different fractal scale algorithm. The results indicate that the fractal scales calculated from Detrended Fluctuation Analysis (DFA) are robust with respect to variation in noise level, Based on the conductance fluctuating signals measured from vertical gas-liquid two phase flow experiment, we calculate the fractal scales of five typical flow patterns. The results show that when the water superficial velocity ranging from 0.0453ms~(-1) to 0.226 ms~(-1) and the gas superficial velocity ranging from 0.0043ms~(-1) to 3.43 ms~(-1), the values of the fractal scale of bubble flow are lowest corresponding to the random complex dynamic behavior, while the values of slug flow are highest corresponding to the alternatively periodic motions between gas slug and liquid slug, and the values of churn flow lies between them indicating the relatively complex dynamic behavior. Our main result is that the fractal scales obtained from conductance fluctuating signals can not only effectively characterize the dynamic characteristics of gas-liquid two phase flow patterns, but also further provide valuable reference for understanding the transitions of different gas-liquid two phase flow patterns.
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