Axisymmetric Synthetic Jets: An Experimental and Theoretical Examination

Abstract

The flowfield of a round synthetic jet driven by a piezoelectric membrane issuing into a quiescent environment is studied in this paper. The self-similar behavior exhibited by both synthetic and continuous turbulent jets leads to the hypothesis that synthetic jetsmay bemodeled using similarity analysis, just as continuous turbulent jets aremodeled. Accordingly, synthetic jets are modeled using both the Schlichting solution to boundary-layer equations in cylindrical coordinates and the Landau–Squire solution to the Navier–Stokes equations in spherical coordinates, for which the virtual viscosity coefficient of a continuous turbulent jet is replaced with that measured for a synthetic jet. The virtual viscosity of the synthetic jet for bothmodels is obtained from the spreading rate and velocity decay rate of the jet. Hot-wire anemometry is used to characterize the flow downstream of the orifice. The flowfield is observed to consist of two regions, as distinguished by the centerline velocity decay: namely, a developing and adeveloped region. The developing region is characterized by a velocity increase followed by a plateau, for which the axial extent of this region scales with the stroke length L. The developed region is identified by the centerline velocity decaying as x , and it is within this region that the jet models are applicable. The velocity decay rate and spreading rate of synthetic jets are observed to increase with stroke ratio L=d, while being independent of the Reynolds number Re. This dependency on stroke ratio is attributed to the increase in impulse and energy of the emerging vortex rings as the stroke ratio increases and their subsequent enhanced interaction. The geometry of the actuator is additionally seen to impact the spreading and decay rates by means of influencing the initial conditions at the orifice. The experiments verify that byusing the adjusted value of the virtual viscosity, the theoreticalmodels of a continuous turbulent jetmay still be used to model a periodic synthetic jet. The virtual viscosity of the synthetic jets under test proves to be larger than that of equivalent turbulent continuous jet based on the same momentum flux. The enhanced viscosity is attributed to the additional momentum transfer and mixing brought about by the periodic introduction and breakdown of the vortex rings in synthetic jets.