Free stream turbulence intensity effects on the flow over a circular cylinder at [formula omitted]: bifurcation, attractors and Lyapunov metric

Abstract

Varying the free-stream turbulence intensity (Ti= 0%, 5%, 10%) the flow over a circular cylinder for Re=3900 is examined using high fidelity eddy-resolving simulations. Results show that with growth of the turbulence intensity, the drag coefficient increases and the pressure base coefficient drops, as well as the flow bifurcation in the near wake occurs, when the length of the separation zone is reduced by about two, and the stream velocity profile is reshaped from U-shaped to V-shaped. The flow transformation is accompanied by the separation of the wall stress scales. At the same time, dynamics of the vortex shedding (Strouhal number) remains unchanged. The flow bifurcation, confirmed experimentally in practice, and the phase transition are examined using the Lyapunov metric (predictability time and phase-space diagrams). The predictability times, i.e. the phase transition between the two states Ti = 0% → 5% and Ti = 0% → 10% are estimated at one half and one of the characteristic convective time, after which the saturation occurs when both dynamical systems reach a statistical stationary state. Finally, phase-space states are visualized in 2D and 3D, and shown that related attractors can be bounded by simple geometrical ellipsoids.