Simulation of Supersonic Nozzle Flows with Plasma-based Control

Abstract

A phenomenological model is employed to mimic the control effects of eight Localized Arc Filament Plasma Actuators (LAFPA) placed around the periphery of a Mach 1.3 nozzle exit. In addition to the axisymmetric (m = 0) mode, the flapping or first mixed (m = ±1) and second mixed (m = ±2) modes are separately introduced at the preferred column-mode frequency corresponding to a Strouhal number of 0.33. No-control and constant excitation cases are also simulated. Comparison with preand post-computation experimental flow visualizations performed at the Ohio State University indicate that the simulations reproduce the main effects generated by the actuators. Detailed analysis with instantaneous, averaged and phase-averaged quantities suggests a complex coherent feature generation, evolution and dissipation process. For m = ±1, the phase-averaged flow reveals successive distorted elliptic vortex rings with axes in the flapping plane, but alternating on either side of the jet axis. This generates a chain of structures where each interacts with its predecessor on one side of the major plane and its successor on the other. Through self and mutual interaction, the leading segment of each loop is pinched and passes through the previous ring before rapidly breaking up, and the mean jet flow takes on an elliptic shape. The m = ±2 mode yields elliptic structures with major axes of successive rings being aligned with the two symmetry planes, which are orthogonal to each other. The minor axis side is pulled downstream faster than the rest of the structure under the possible influence of the higher velocity near the jet centerline and self-induced effects, yielding a horse-shoe shape when viewed in profile. The mean jet structure evolves from a “+” shaped cross-section to a square and then roughly circular profile as it dissipates. The m = 0 mode exhibits relatively stable roll-up events, with vortex ribs in the braid regions connecting successive large coherent structures. The constant excitation and no-control cases are similar to each other. In terms of mixing, of the modes examined, them = ±1mode is confirmed to show the most rapid decline of centerline Mach number, followed by them = ±2 mode.