The role of vibrations for reducing the resistance in the relative movement of parallel plates

Abstract

The effect of surface vibrations on the propulsion augmentation and resistance in the relative movement of parallel plates has been studied. The analysis was focused on monochromatic waves and laminar flows. The effectiveness of the vibrations was gauged by determining the external force required to maintain the movement of one of the plates at a prescribed velocity. It is shown that waves propagating upstream always increase the resistance but the flow response to waves propagating downstream is more intricate and is a function of the flow Reynolds number. In general, waves must be sufficiently fast to reduce the flow resistance. This leads to a natural division between slow and fast waves; a characterization that is helpful for flows at a sufficiently small Reynolds number Re. An increase in Re brings into play the complication of possible resonances with the natural flow frequencies. Resonances are not possible with waves faster than the plate velocity and these supercritical waves generally decrease the flow resistance. More complex flow responses can occur with slower (subcritical) waves which tend to increase the flow resistance. A complete elimination of the resistance is possible if the waves are of sufficiently short wavelength and travel quickly. This suggests that our mechanism has great potential in the development of propulsion augmentation systems. None of the waves produced net energy savings.