Strength and timing of primary and secondary vortices generated by a rotating plate

Accurate predictions of how vortices grow, evolve, and separate from aerodynamic objects are desirable for various applications ranging from autonomous aerial vehicles to wind turbines. Here, we present an experimental characterisation of the formation process of vortices created by the rotation of a thin rectangular flat plate. The plate is rapidly accelerated from rest up to a constant rotational velocity that was varied to explore the effect of the Reynolds number on the limit strength and the timing of successively generated vortices at the tip of the plate. The total non-dimensional positive circulation released at the tip of the plate during the entire rotation varies solely as a function of the angular position of the plate. Initially, all this circulation accumulates in a primary or starting vortex until this vortex separates after a constant non-dimensional time for all rotational velocities and different plate dimensions tested. An empirical model of the prediction of the limit strength of the primary vortex based on the constant non-dimensional formation is presented. The limit strength of the primary vortex is independent of the Reynolds number. After the primary vortex separates, a series of smaller secondary vortices form at the tip of the plate. These secondary vortices are discretely released at increasing time intervals. The timing of the release of the secondary vortices and their non-dimensional strength depend on the Reynolds number, and an empirical prediction model is presented.