Phase-based control of periodic flows

Unsteady bluff-body flows exhibit dominant oscillatory behaviour owing to periodic vortex shedding. The ability to manipulate this vortex shedding is critical to improving the aerodynamic performance of bodies in a flow. This goal requires a precise understanding of how the perturbations affect the asymptotic behaviour of the oscillatory flow and of the ability to control transient dynamics. In this work, we develop an energy-efficient flow-control strategy to alter the oscillation phase of time-periodic fluid flows rapidly. First, we perform a phase-sensitivity analysis to construct a reduced-order model for the response of the flow oscillation to impulsive control inputs at various phases. Next, we introduce a real-time optimal phase-control strategy based on the phase-sensitivity function obtained by solving the associated Euler–Lagrange equations as a two-point boundary-value problem. Our approach is demonstrated for the incompressible laminar flow past a circular cylinder and an airfoil. We show the effectiveness of phase control with different actuation inputs, including blowing and rotary control. Moreover, our control approach is a sensor-based approach without the need for access to high-dimensional measurements of the entire flow field.