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

TL;DR

This study explores the turbulent wake of the fluidic pinball, a benchmark for flow control, revealing complex bifurcations and control limits at high Reynolds numbers through experiments and simulations.

Contribution

First comprehensive experimental and numerical analysis of turbulent wake dynamics and bifurcations of the fluidic pinball at Re=9100, expanding understanding beyond laminar regimes.

Findings

Turbulent wake can be modeled by a three-dimensional bifurcation manifold.

Identification of a new low-frequency shedding state in the boat-tailing limit.

Control authority diminishes in the boat-tailing regime with distinct flow dynamics.

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.