On the chaotic nature of bistable flows

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Evidences from experimental measurements in tube banks submitted to turbulent cross flow in quadrangular and triangular arrangements show the presence of instabilities, being associated to the phenomenon of bistability, known in the simplified case of the flow on two cylinders side-by-side. Although not completely understood the study of the dynamic process of bistability can reveal new features about the chaotic behavior of these time series. As chaotic time series are observed routinely in experiments on physical systems, a study of the characteristics of bistability can be performed with the aid of techniques already established. This work presents a study about the determination of the Lyapunov exponents from experimental time series of bistable flows on the simplified geometry of two parallel circular cylinders and on a set of rows of a triangular tube bank. Time series of flow velocity and velocity fluctuations were obtained by means of the constant hot-wire anemometry technique in an aerodynamic channel. Discrete wavelet transform was used to make a multilevel decomposition of the series in several bandwidth values, accordingly with a selected decomposition level. Thus, the turbulence can be dissociated from the original signals, allowing a more accurate study to be conducted on the obtained state spaces. With these filtered time series, a state space reconstruction was performed by the method of time delays or Takens’ method, while the percentage of false neighbors together with the embedding dimension were useful for the choice of some of the analysis parameters. The Rosenstein’s method was applied to calculate the largest Lyapunov exponent of the time series. Easy to implement, this method is robust with respect to changes in most immersion parameters. Results show that the flow after two circular cylinders placed side-by-side and after two rows tube bank in triangular arrangement present positive largest Lyapunov exponents. This means that bistability has a clear chaotic behavior. In contrast, the flow after a five row tube bank is random.