Chaotic dynamics of large-scale structures in a turbulent wake

Abstract

The dynamics of a 3D bimodal turbulent wake downstream a square-back Ahmed body are experimentally studied in a wind-tunnel through high-frequency wall pressure probes mapping the rear of the model and a horizontal 2D velocity field. The barycenters of the pressure distribution over the rear part of the model and the intensity recirculation are found highly correlated. Both described the most energetic large-scale structures dynamics, confirming the relation between the large-scale recirculation bubble and its wall pressure foot-print. Focusing on the pressure, its barycenter trajectory has a stochastic behavior but its low frequencies dynamics exhibit the same characteristics as a weak strange chaotic attractor system, with two well defined attractors. The low frequencies dynamics associated to the large-scale structures are then analyzed. The largest Lyapunov exponent is first estimated, leading to a low positive value characteristic of strange attractors and weak chaotic systems. Afterwards, analyzing the autocorrelation function of the time-series, we compute the correlation dimension, larger than two. The signal is finally transformed and analyzed as a telegraph signal showing that its dynamics correspond to a quasi-random telegraph signal. This is the first demonstration that the low frequencies dynamics of a turbulent 3D wake are not a purely stochastic process but rather a weak chaotic process exhibiting strange attractors. From the flowcontrol point of view, it also opens the path to more simple closed-loop flow control strategies aiming at the stabilization of the wake and the control of the dynamics of the wake barycenter.

Adaptive control of the dynamics of a fully turbulent bimodal wake using real-time PIV

“…The bluff body is a 0.7 scale of the original Ahmed body Ahmed et al (1984): it is L = 0.731 m long, H = 0.202 m high and W = 0.272 m wide, as described in Varon et al (2017). The rear part of the model is a square-back geometry with sharp edges leading to a massive separation of the flow and to the creation of a large 3D recirculation bubble over the rear part of the model.…”

“…Recently, it was shown that the large-scale slow-time oscillations behaves like a high dimensional chaotic system with a well-defined strange attractor (Varon et al, 2017). This result was obtained through the analysis of the timeseries of the coordinate of the barycenter of the wall-pressure field measured over the rear vertical part of the model.…”

“…PIV is well suited for that since it is a noninvasive method. Furthermore, to monitor the bimodal behavior it is possible to relate quantities derived from velocity fields (spanwise component, fluctuations or recirculation intensity barycenter) to quantities derived from base pressure (pressure center or pressure gradient) Volpe et al, 2015;Varon et al, 2017). We need thus to fast compute the velocity fields and their derived quantities.…”

Evolution of the bi-stable wake of a square-back automotive shape

“…They are not a reconstruction of a particular periodic behaviour, as the succession of the bi-stable states seems to be a weak chaotic process (Varon et al 2017). Nevertheless, they still provide insights into how the wake evolves between states.…”

“…In these conditions, it was found that the characteristic time between switches can be estimated as T l ∼ 10 3 H∕V ∞ , where V ∞ is the freestream velocity. The succession of reflectional symmetry breaking states was initially thought to behave like a stationary Markov chain, although more recent findings from Varon et al (2017) suggest that the low-frequency dynamics may be considered as a weak chaotic process with two attractors. In Grandemange et al (2013b), it is also shown that this long period motion yields an unsteady side force that was inferred to be responsible for part of the drag.…”