Three dimensional simulations of a feedback controlled circular cylinder wake Jürgen Seidel * , Stefan Siegel † , Kelly Cohen ‡ , Thomas McLaughlin § Department of Aeronautics, U.S. Air Force Academy, Colorado Springs, CO 80840, USA Three dimensional open loop and closed loop feedback control simulations of the wake behind a circular cylinder are analyzed to explore the effect of spanwise phase variations. For feedback control, a low dimensional model based on Proper Orthogonal Decomposition (POD) in conjunction with a Least-Squares Estimation is used to estimate the flow state in the center plane behind the cylinder. In two dimensional simulations, we observed that at low Reynolds numbers (100 or less), the von Karman Vortex Street can be strengthened or weakened depending on the phase shift applied in the controller. At higher Reynolds numbers, if the vortex shedding is weakened, spanwise phase variations eventually lead to loss of control. The current computations show that the sensor plane can be successfully controlled for all cases. However, the vortices in other spanwise planes are out of phase and are amplified. Clearly, spanwise observability is necessary to stabilize the wake in three dimensions. Nomenclature A = Amplitude of oscillation a i = POD mode amplitude D = Cylinder diameter f = Frequency i = Index K = Feedback gain K p = Proportional feedback gain K d = Differential feedback gain K a = Amplitude gain K ϕ = Phase gain M = Mach number Re = Reynolds number based on cylinder diameter t = Time U = Free stream velocity u = Mean velocity x,y,z = Streamwise, normal, and spanwise coordinate directions y cyl = Cylinder displacement ∆t = Time step ϕ = Phase advance angle Φ i = Spatial POD mode * Visiting Researcher, Department of Aeronautics, Member † Assistant Research Associate, Department of Aeronautics, Senior Member ‡ Visiting Researcher, Department of Aeronautics, Senior Member § Director, Aeronautics Research Center, Department of Aeronautics, Associate Fellow 43rd AIAA Aerospace Sciences Meeting and Exhibit 10 - 13 January 2005, Reno, Nevada AIAA 2005-295 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Downloaded by UNIVERSITY OF CINCINNATI on December 7, 2014 | http://arc.aiaa.org | DOI: 10.2514/6.2005-295