Reduced-order modeling of the fluidic pinball

Luc R Pastur (1) , Nan Deng (1, 2) , Marek Morzyński (3) , Bernd R Noack (4, 5)

1 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
2 LISN - Laboratoire Interdisciplinaire des Sciences du Numérique
3 PUT - Poznan University of Technology
4 HIT - Harbin Institute of Technology
5 Institut für Strömungsmechanik und Technische Akustik

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 lowestorder model made of three degrees of freedom.

Mots clés: fluid mechanics; flow control; reduced-order modeling; transition to chaos

Domaines: Science non linéaire [physics]; Dynamique des Fluides [physics.flu-dyn]; Mécanique des fluides [physics.class-ph]

Luc R Pastur, Nan Deng, Marek Morzyński, Bernd R Noack. Reduced-order modeling of the fluidic pinball. 11th Chaotic Modeling and Simulation International Conference, pp.205-213, 2019, ⟨10.1007/978-3-030-15297-0_19⟩. ⟨hal-03195620⟩