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We present and discuss results on the development and application of extremizing feedback control to high-speed and high Reynolds number axisymmetric jets. In particular, we demonstrate control authority on the near-field pressure of a Mach 0.9 jet with a Reynolds number based on jet diameter of 6.4 c [10.sup.5]. Open-loop forcing experimental results are presented, wherein localized are filament plasma actuators are shown to have two distinct effects on the irrotational near-field pressure, similar to their effects on the far-field acoustics reported earlier. At low forcing Stroubal numbers near the jet preferred mode, a large amplification in the pressure fluctuations is observed. At much higher forcing Strouhal numbers, an attenuation is observed in the pressure fluctuations over a broad range of excitation frequencies, especially in the axisymmetric mode of the pressure fluctuations. Previous experiments have shown that forcing the jet with these low and high Strouhal numbers results in jet mixing enhancement and farfield noise reduction, respectively. Two different gradient-free extremizing feedback control algorithms have been developed and implemented, each of which can perform online minimum seeking, as well as maximum seeking. Both methods demonstrate fast convergence to the optimum followed by steady operation. We also show that the far-field acoustic spectrum in steady-state operation of the closed-loop control is quite similar to that observed with optimal open-loop forcing. DOI: 10.2514/1.44012

A theoretical analysis is carried out to predict the amplification of turbulence in flows experiencing one-dimensional and axisymmetric dilatations. When three representative vortices are tracked, the variations of vortex radius and vorticity are calculated, and then the amplification of turbulence is obtained from them. When a vortex is tracked, conservation laws of mass and angular momentum of the vortex are used. For a one dimensionally compressed flow, the present analysis slightly underestimates the amplification of velocity fluctuations and turbulent kinetic energy, relative to that of rapid distortion theory in the solenoidal limit. For an axisymmetrically distorted flow, the amplification of velocity fluctuations and turbulent kinetic energy and the anisotropy depend not only on the density ratio, but also on the ratio of streamwise mean velocities, which represents streamwise vortex contraction/stretching. The amplification predicted by the present analysis is in excellent agreement with that by the rapid distortion theory. In both flows, the amplification of turbulence is dictated by the mean density ratio, whereas the anisotropy is primarily dictated by the flow boundary. However, streamwise vortex stretching/contraction alters the amplification slightly and the anisotropy significantly in the axisymmetric flow.

The effects of bulk expansion and compression on turbulence levels in supersonic boundary layers were predicted using the law of angular momentum conservation. For the compression case the present analysis predicted the amplification of turbulence level quite well when the effect of extra strain rate caused by the streamline curvature is small, where it was estimated that 90-95% of the increase in the turbulence level is caused by the bulk compression. When extra strain rate effects are present, however, the contribution of the bulk compression on the total turbulence level was reduced to about 85-90%. The predicted general trend of turbulence amplification with increasing flow-turning angle, which seems to be closely related to the linear increase in the mean density, agrees well with that of other researchers. For the expansion case, however, a quantitative comparison was challenging because the available experimental data were taken too close to the end of the perturbation region, thus not showing the relaxation behavior. In both compression and expansion flows the bulk dilatation was found to be the dominant factor responsible for the changed turbulence intensity.