Symbolic Dynamics Applied to the Identification of Flow Patterns Inside Tube Banks

This paper presents a study of the identification of flow patterns inside a tube bank with the technique of symbolic dynamics. The experimental signals of the mean velocity and its fluctuations are measured by hot-wire anemometry in an aerodynamic channel and used as input data for the symbolic dynamics technique. The tube bank consists of 23 circular cylinders in a triangular arrangement. The pitch-to-diameter ratio chosen was 1.26 and the Reynolds numbers are in the range from 7.5 × 10³ to 4.4 × 10⁴, computed with the tube diameter, D = 25.1 mm, and the percolation velocity. In this work, a binary alphabet was chosen to convert and analyze the data. The partitioning process is performed through the mean value of the time series and via discrete wavelet reconstruction, according to a chosen reconstruction level. The flow patterns are presented for different positions inside the tube bank, where histograms and probability density functions support the statistical interpretation. The histograms with a decimal representation for the original experimental time series with partitioning performed through the mean value show that the signals do not present fast changes of velocity fluctuations. This behavior was observed in the five rows of cylinders. However, by changing the partitioning according to a wavelet reconstruction of the signal with high frequency, which means that the signals are close to the partitioning function, fast changes appear in all of the time series observed. The results indicate that the turbulence in tube banks has chaotic characteristics. Flow visualizations performed with ink injection inside the tube bank helped in the interpretation of the results.