New Wake Models With Capability of Capturing Nonlinear Physics

We developed reduced-order models for the wake (in terms of the amplitude of the induced lift force) of a forced circular cylinder using analytical techniques. We first considered several forced oscillators (existing and proposed) and evaluated their suitability to model the synchronized wake, where the lift frequency is synchronized with the forcing frequency. These forced oscillators differ in the nature of the forcing terms used to represent the influence of the cylinder motion on the lift. Existing wake oscillators for a moving cylinder do not capture the important nonlinear phenomena, such as the multi-valuedness and the abrupt changes that occur as the parameters (e.g., the reduced velocity) change. These phenomena occur when one mode of the wake loses stability through a bifurcation to another mode. We then proposed two new oscillators that are capable of generating the correct wake response over the entire frequency range of synchronization even across the discontinuity. The forcing terms are a combination of external and parametric terms. Current models use only external (ideal) forcing, which we show to be insufficient. We then investigated the effect of the oscillators parameters on the modeled lift.