A Lagrangian Perspective on Vortex Formation for Unsteady Flat Plates

An investigation into the interdependency between acceleration and vorticity fields for rapidly accelerating, AR=4 plates with varying kinematics and initial conditions has been performed. In addition, the vorticity redistribution and reorientation in the plate’s proximity has also been studied. The data was obtained simultaneously by means of a threedimensional particle tracking velocimetry (3D-PTV) system together with a six-component force sensor. The effective velocity of the feeding shear layer has been identified as the appropriate characteristic velocity rather than the more commonly-used plunge or freestream velocities. Based on these newly-normalized circulation histories, it has been demonstrated that the existence of initial boundary-layer vorticity on the plunging plate - at least in the near midplane region - does not contribute to the eventual vortex formation. The comparison of identical plate kinematics with and without a superimposed uniform freestream velocity revealed a close interdependency of vorticity and Lagrangian acceleration fields. Consequently, a separation and/or superposition of circulatory and non-circulatory effects leads to an oversimplified description of such separated flows. In accordance with literature, the tip vortex has been identified to be an important contributor in the overall force production. Tip-vortex strength as well as its relative positioning to the plate surface influences the instantaneous force. As such, the orientation of the tip vortex becomes the critical contributor to lift once the acceleration of the plate has ceased.