Phase-resolved flow field produced by a vibrating cantilever plate between two endplates

Abstract

The flow field created by a vibrating cantilever plate was studied using phase-resolved particle image velocimetry measurements as well as a smoke visualization technique. The cantilever is 38 mm wide, 31 mm long, and is actuated by a piezoelectric material. It is immersed in initially quiescent air, i.e., no free stream velocity is imposed on the system. The cantilever’s vibration frequency in these experiments is set to 180 Hz—the fundamental natural frequency of cantilever. The flow is quite complicated in nature. During each vibration cycle a pair of counter-rotating vortices is generated. A high velocity region is formed between these two counter-rotating vortices in which the maximum velocity is nearly four times the maximum speed of the free end of the plate. Front and rear walls are installed at the lateral edges of the cantilever initially with the thought of making the flow quasi-two-dimensional. While a two-dimensional flow field is indeed formed near the cantilever tip, the flow downstream of the tip is complex and three-dimensional. Phase-resolved velocity fields for five different amplitudes are acquired in detail. The corresponding Reynolds numbers Reh based on the cantilever tip vibration amplitude and the tip speed are 146, 126, 101, 72, and 43, respectively. The nondimensionalized velocity fields are almost identical and symmetric near the tip, but asymmetric flows are formed and the nondimensionalized velocity fields are no longer identical further downstream of the tip. The time dependent circulation of each vortex is calculated by applying the general theory of oscillating, deformable airfoils and compared to the experimental circulation.