Proper orthogonal decomposition analysis of vortex dynamics of a circular cylinder under synthetic jet control

Abstract

Vortex dynamics of a circular cylinder controlled by a synthetic jet positioned at the back stagnation point is experimentally investigated using particle image velocimetry (PIV) technique. The proper orthogonal decomposition (POD) method is adopted to present the variations of the POD energy, mode, coefficient, corresponding dominant frequency, and the reconstructed spanwise vorticity. It is found that the dominant dimensionless control parameters should be the synthetic jet stroke length L0/D, where D is the diameter of the experimental circular cylinder, and the equivalent momentum coefficient Cμ. For the same stroke length L0/D=3.3, the states of the wake vortex shedding are determined by the momentum coefficient. They can be categorized into three groups summarizing all the parameters tested: antisymmetric Karman vortex shedding mode (Cμ≤0.027), vortex synchronization with shedding modes varying between the symmetric and antisymmetric ones (0.061≤Cμ≤0.109), and vortex synchronization with symmetric shedding mode (0.213≤Cμ≤0.378). When the symmetric shedding mode occurs, the corresponding spanwise vorticity modes show two parallel rows of half-arrowhead structures with alternate signs that are antisymmetric about the centerline. The POD modes based on the streamwise and vertical velocities also exhibit regular variations with different wake vortex shedding states.