Reduced-order modeling of the fluidic pinball

TL;DR

This paper develops a reduced-order model for the fluidic pinball, a flow system with three rotating cylinders, capturing its primary Hopf bifurcation and vortex shedding dynamics efficiently.

Contribution

It introduces a low-dimensional model based on dynamically consistent modes that accurately describes the flow's primary bifurcation behavior.

Findings

The flow undergoes a Hopf bifurcation leading to vortex shedding.

A three-degree-of-freedom model captures the main dynamics.

The model enables rapid testing of flow control laws.

Abstract

The fluidic pinball is a geometrically simple flow configuration with three rotating cylinders on the vertex of an equilateral triangle. Yet, it remains physically rich enough to host a range of interacting frequencies and to allow testing of control laws within minutes on a laptop. The system has multiple inputs (the three cylinders can independently rotate around their axis) and multiple outputs (downstream velocity sensors). Investigating the natural flow dynamics, we found that the first unsteady transition undergone by the wake flow, when increasing the Reynolds number, is a Hopf bifurcation leading to the usual time-periodic vortex shedding phenomenon, typical of cylinder wake flows, in which the mean flow field preserves axial symmetry. We extract dynamically consistent modes from the flow data in order to built a reduced-order model (ROM) of this flow regime. We show that the main dynamical features of the primary Hopf bifurcation can be described by a non-trivial lowest-order model made of three degrees of freedom.