A fractal approach for interpretation of local instantaneous temperature signals around a horizontal heat transfer tube in a bubbling fluidized bed

Temperature signals measured around a horizontal heat transfer tube in a bubbling fluidized bed have been analyzed using Hurst's rescaled range (R/S) analysis. This analysis estimates and identifies long-term persistence or correlation in measured time series. The Hurst exponent H, which is evaluated from R/S analysis, also provides the local fractal dimension of the time series. A new approach to analyze an air fluidized particle system is proposed based on the evaluation of the Hurst exponent. Two Hurst exponents can be evaluated from a single time series, one from the discrete time fractional noise (where the linearity of the signal is subtracted and short-term fluctuations are emphasized) and the other from the signal itself (without subtracting the linearity of the signal). The authors argue that the Hurst exponent obtained from discrete time fractional noise characterizes the particle motion, whereas the Hurst exponent obtained from the signal itself characterizes the bubble motion. Moreover, a comparison between these two Hurst components identifies the zones where an alternating type of contact between the tube surface and the bubble-emulsion phase occur. The results were interpreted in conjunction with the mutual information function. The mutual information function provides the relationship between the data points separated in time and uses only the statistical relationship between the data points. The mutual information functions and the Hurst exponents exhibited similar trends around the heat transfer tube.