Chaotic time series analysis of dynamical behavior for low frequency fluctuations in torque in agitated vessel

To clarify very low frequency fluctuations in the torque in an agitated vessel, the dynamical behavior of the torque fluctuations was examined from power spectrum analysis and chaotic time series analysis of the measured torque time series in an agitated vessel with paddle impellers. The maximum Lyapunov exponent of the very low frequency torque fluctuations in an agitated vessel had positive value, which means that the fluctuations have the chaotic nature. The critical value of the fractal dimension of the fluctuation decreased and the irregular frequency region became larger with an increase in the rotational speed in the region of 1.0-2.0 s(-1). The magnitude of the fractal dimension increased with an increase in the aspect ratio.