Sensitivity of the least stable modes to passive control for a flow around an elastically mounted circular cylinder

This paper presents a methodology to calculate the sensitivity of the least stable eigenvalues with respect to an external forcing added in a fluid-structure interaction system. The structure is a rigid circular cylinder. The algorithms were implemented using the spectral/hp element method for the spatial discretization. We make use of the adjoint equations of the flow-structure coupled system to provide the regions more receptivity to an external forcing. Next, sensitivity computations are carried out by setting the external forcing proportional to the flow velocity and applied in a local point in the domain. The fields of sensitivity were analyzed by using the two least stable modes for different values of reduced velocity. The results were compared to those obtained for a fixed cylinder at the same Reynolds number. Our main findings reveal that the sensitivity fields of the fluid-structure interaction system can be very different from its fixed structure counterpart, and among the cases, with an elastic structure, the fields vary according to the reduced velocity. The sensitivity results were verified against linear and nonlinear simulations of flows with small control cylinders placed at locations selected according to the sensitivity fields. The agreement between the predictions made with the sensitivity analyses and the linear and nonlinear results of the forced flows was excellent. Furthermore, evaluating the sensitivity predictions based on the two least stable modes can be essential if the goal is attenuate the vortex-induced vibration.