Instability of cylinder wake under open-loop active control

Abstract

Instability of a wake controlled by a streamwise Lorentz force is investigated through a Floquet stability analysis. The streamwise Lorentz force, which is a two-dimens- ional control input created by an electromagnetic actuator located on the cylinder surface, adjusts the base flow to affect the three-dimensional wake instability and achieve wake stabilization and transition delay. The instability mode at a Reynolds number Re = 300 can be transformed from B to A with N = 1.0, where N is an interaction number repre- senting the strength of the Lorentz force relative to the inertial force in the fluid. The wake flow is Floquet stable when N increases to 1.3. The spanwise perturbation wavelengths are 3.926D and 0.822D in the modes A and B, respectively, where D is the cylinder diameter. In addition, the oscillating amplitudes of drag and lift are reduced with the increase in the interaction number. Particle tracing is used to explore the essential physical mechanism for mode transformation. The path lines show that suppression of flow separation hinders the fluid deformation and rotation, leading to the decrease in elliptic and hyperbolic instability regions, which is the material cause of mode transformation. All of the results indicate that wake stabilization and transition delay can be achieved under open-loop active control via the streamwise Lorentz force.