Effects of a synthetic jet acting on a separated flow over a hump

The effects of an oscillatory zero-net-mass-flux jet (i.e. synthetic jet) acting on a separated flow over a hump are investigated in terms of two actuation parameters – actuator position and forcing frequency. By considering the vorticity flux balance and introducing a centroid of vorticity production over the hump surface, lift and drag acting on the hump can be expressed as a function of this centroid and the rate of vorticity production. To study the parametric dependence of lift and drag, direct numerical simulation (DNS) is performed by solving compressible, unsteady, laminar flows over a half-cylindrical hump in two dimensions. The DNS results show that periodic actuation significantly reduces the rate of vorticity production at the wall and shifts the centroid upstream so that the drag is reduced and the lift is increased, respectively. When the actuation parameters are varied, it is found that the lift is governed by the horizontal coordinate of the vorticity-production centroid, while the drag is determined by both the vertical coordinate of the centroid and the rate of vorticity production over the hump. This paper explains by using ideal flow models that the vorticity-production centroid is controlled by two factors: one is the actuator position at which clockwise vorticity is generated, and the other is the point where the separation vortex is pinched off, thereby the clockwise vorticity being absorbed

A refinement of Johnson's bounding for the stable genera of Heegaard splittings

For each integer k > 1, Johnson gave a 3-manifold with Heegaard splittings of genera 2k and 2k-1 such that any common stabilization of these two surfaces has genus at least 3k-1. We modify his argument to produce a 3-manifold with two Heegaard splitings of genus 2k such that any common stabilization of them has genus at least 3k.Comment: 16 pages, 17 figure