Floquet Instability in Periodically Reversing Flows

Current 3-D finite-state wake models are incapable of simulating a maneuver in which the sign of the free-stream velocity changes direction and the rotor enters its own wake - as might occur in the case of a helicopter which ascends and then descends. It is the purpose of this work to create a 2-D finite-state wake model which is capable of handling changes in free-stream direction as a precursor to development of a 3-D model that can do the same. The 2-D finite-state model used for reentry modifications is an existing model created by Peters, Johnson, and Karunamoorthy. By the addition of a parameter which changes the sign of the free-stream accordingly, a model capable of handling forward and backward flight is developed and tested. Upon testing of the model for an oscillatory free-stream which changes direction, it was discovered that the presence of a singularity causes the system to become unstable. This behavior was determined to be due to a Floquet instability which occurs in periodic free-streams that reverse direction.