On the turbulent wake of the actuated fluidic pinball: dynamics, bifurcations and control authority

Abstract

We present the first comprehensive experimental and numerical study featuring the turbulent wake of the fluidic pinball for a large actuation range. The fluidic pinball is a cluster of three equal circular cylinders centered on the vertices of an equilateral triangle, pointing upstream in uniform flow. This configuration has become a canonical benchmark for control-oriented reduced-order modeling, for nonlinear control design and for a large kaleidoscope of drag reduction mechanisms. While the literature covers well the laminar two-dimensional Reynolds number regime, we focus on unexplored terra incognita: experiments of the symmetrically actuated turbulent regime at a Reynolds number of Re=9100. In other words, the upstream cylinder is kept stationary, while the two downstream cylinders rotate with equal and opposite angular velocities. A large range of base-bleeding and boat-tailing actuation parameters is investigated with time-resolved particle image velocimetry and aerodynamic force measurement with a companion Reynolds-averaged Navier-Stokes simulation. Our results indicate that the turbulent wake of the fluidic pinball can be approximated by a three-dimensional actuation manifold comprising two inverse pitchfork bifurcations. In the boat-tailing limit, a reduced control authority with a new low-frequency shedding state is observed.

Figures (8)

• Figure 1: Schematics of the experimental setup. (a) Two-dimensional representation of the fluidic pinball with main dimensions and nomenclature. The blue area depicts the PIV measurement domain. The brown squares represent the turbulators placed upstream of the cylinders. (b) Side view of the arrangement. (c) Top view of the lower plate where the load cells are mounted.
• Figure 2: Mesh used in the URANS simulations.
• Figure 3: Contour representation of the time-averaged velocity magnitude in the wake of the fluidic pinball under symmetric actuation, with superposed LIC representation of the mean velocity field. Dashed colored lines identify the actuation cases. For the unforced case (a,d), the gap jet deflects upward or downward, producing two quasi-steady asymmetric wakes. Increasing $p$ (b,c) suppresses the gap jet and narrows the wake, whereas decreasing $p$ (e,f) strengthens a central jet that divides the wake into two lateral branches.
• Figure 4: Cumulative normalized POD energy as a function of mode number for six actuation cases: base bleeding, unforced, and boat tailing. The energy of the first 200 modes of the baseline case $p=0\ \downarrow$ is used for the normalization.
• Figure 5: First POD spatial mode and leading oscillatory pair associated with the dominant vortex-shedding dynamics, together with their corresponding temporal coefficients for representative actuation cases: (a) base bleeding $p=-2.2$, modes 1-3; (b) baseline $p=0$, modes 1-3; (c) weak boat tailing $p=1.4$, modes 1-2; (d) strong boat tailing $p=2.2$, modes 1-2. Line styles and colors uniquely identify the POD modes. The same color and line style are consistently used for each spatial mode and its corresponding temporal coefficient.