Power spectrum and fractal dimension analyses for low frequency fluctuations in the torque time series in an agitated vessel

To clarify very law frequency fluctuations in the torque time series in an agitated vessel, the magnitude and periodicity of the fluctuations were exa mined from power spectrum analysis and autocorrelation function analysis of the measured torque time series in an agitated vessel with paddle impeller s. The fluctuations consisted of quasi-periodic motions with three frequenc ies, blade passage frequency, rotation frequency, and another frequency (th e third frequency), and a nonperiodic and very low frequency motion which w as about 290 times long as that of the blade passage frequency. The fluctua tion was fractal nature from fractal dimension analysis using the Higuchi m ethod. The correlation dimension of the fluctuation had a non-integer value in the range 3.9-5.2 from correlation dimension analysis using the Grassbe rger-Procattia method. From these results, it is concluded that the very lo w frequency fluctuations in the torque time series in an agitated vessel ca n be described with a deterministic method.