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 Particular Solution of a Painlev\'e System in Terms of the Hypergeometric Function n+1Fn{}_{n+1}F_n

In a recent work, we proposed the coupled Painlev\'e VI system with $A^{(1)}_{2n+1}$-symmetry, which is a higher order generalization of the sixth Painlev\'e equation ($P_{\rm VI}$). In this article, we present its particular solution expressed in terms of the hypergeometric function ${}_{n+1}F_n$. We also discuss a degeneration structure of the Painlev\'e system derived from the confluence of ${}_{n+1}F_n$

Instability waves in a subsonic round jet detected using a near-field phased microphone array

We propose a diagnostic technique to detect instability waves in a subsonic round jet using a phased microphone array. The detection algorithm is analogous to the beam-forming technique, which is typically used with a far-field microphone array to localize noise sources. By replacing the reference solutions used in the conventional beam-forming with eigenfunctions from linear stability analysis, the amplitudes of instability waves in the axisymmetric and first two azimuthal modes are inferred. Experimental measurements with particle image velocimetry and a database from direct numerical simulation are incorporated to design a conical array that is placed just outside the mixing layer near the nozzle exit. The proposed diagnostic technique is tested in experiments by checking for consistency of the radial decay, streamwise evolution and phase correlation of hydrodynamic pressure. The results demonstrate that in a statistical sense, the pressure field is consistent with instability waves evolving in the turbulent mean flow from the nozzle exit to the end of the potential core, particularly near the most amplified frequency of each azimuthal mode. We apply this technique to study the effects of jet Mach number and temperature ratio on the azimuthal mode balance and evolution of instability waves. We also compare the results from the beam-forming algorithm with the proper orthogonal decomposition and discuss some implications for jet noise