Lagrangian analysis on structure evolution and mass transport of circular and noncircular turbulent synthetic jets

Fluid entrainment is of particular significance for the applications of synthetic jets in flow control. We investigate the structure evolution and transient fluid entrainment by the vortex rings in turbulent synthetic jets. Two orifice configurations of circular and rectangular with the aspect ratio of 3 are examined at the same parameters. Time-resolved tomographic particle image velocimetry is used to acquire the three-dimensional flow field information. The analysis based on Lagrangian coherent structures is used to visualize topology deformation of the vortex ring, describe mass transport and quantify entrainment by successive vortex rings. Particularly, the traditional method of the moving reference frame of the vortex ring cannot be effectively applied to the rectangular case due to non-uniform azimuthal translational velocity on the vortex ring. A new approach based on identifying the vortex boundaries by the finite-time Lyapunov exponent ridges is adopted to estimate the volume of the vortex bubble and thus to calculate entrainment and kinetic energy fractions. The results show that the rectangular case generally entrains more ambient fluids, resulting in larger vortex strength than the circular case. Furthermore, more kinetic energy from the ejected fluids is absorbed by the rectangular case to sustain the axis switching of the vortex ring. That could be beneficial for jet mixing enhancement. The current study develops the mathematic description of the dynamics of vortex rings, which can provide an important reference for quantifying fluid entrainment by the vortex rings in flow control applications. [Figure not available: see fulltext.].