Stabilizing the flow past twin cylinders using rotation

For modest Reynolds numbers, the steady-state flow past twin (side-by-side) cylinders (separated by a diameter) is unstable. This flow can be stabilized for Reynolds numbers up to 66 by using cylinder rotation. We investigate the quality of the controlled flow when using linear, quadratic, or cubic feedback that are computed using the quadratic-quadratic regulator formulation and the accompanying QQR software. The cubic feedback law is able to more effectively stabilize the flow while also requiring less control energy to do so. For Reynolds numbers 67 and above, an additional asymmetric unstable mode appears and the actuation mechanisms are not sufficient. Similarly, for larger spacing between the cylinders, the antiphase synchronized vortex shedding can also not be stabilized with the rotational actuation mechanism. This agrees with the recent study of these flows by Carini et al. (JFM, 2014). Thus an additional actuation mechanism, such as inflow perturbation or mass injection is required for these cases.