Localized arc filament plasma actuators have demonstrated significant potential in controlling high-speed and high Reynolds number jets in open-loop. The two primary goals of jet control are either noise reduction or bulk mixing enhancement. This research develops the tools for implementing feedback for this flow control system. The particular jet considered is a Mach 0.9 axisymmetric configuration with Reynolds number 670,000.
The jet near-field pressure is well-suited for real-time non-intrusive observation of the flow state. Its response to forcing is similar to that of the far acoustic field. Forcing near the jet column mode results in amplification; forcing close to the shear layer mode yields attenuation. As a preliminary effort, two model-free feedback control algorithms are developed and implemented for online optimization of the forcing frequency to extremize the near-field pressure fluctuations. The steady-state behavior of the jet under closed-loop control matches the optimal open-loop results. However, the responsiveness of the controllers is poor since the dynamics of the jet are neglected.
The first step in model-based feedback control is the development of a reduced-order model for the unforced jet. A cylindrical domain spanning the end of the jet potential core is chosen for the significance of its dynamics to the applications at hand. A combination of proper orthogonal decomposition and Galerkin projection is used to reduce the Navier-Stokes equations into a small set of ordinary differential equations employing empirical data. Extensive validation is performed on two existing numerical simulation databases of jets spanning low and high Reynolds numbers, and subsonic and supersonic speeds. Subsequently, a 35-dimensional model is derived from experimental data and shown to capture the most important dynamical aspects. The short-term prediction accuracy is found to be acceptable for the purpose of feedback control. The statistics from intermediate-term simulations also display good agreement with experimental observations. However, the simulated trajectories from the model grow unbounded beyond about 50 flow time steps.
The model of the unforced jet is augmented to incorporate the effects of plasma actuation. The periodic forcing is modeled as a deterministic pressure wave specified on the boundary of the modeling domain. Forcing of the 35-dimensional model around the jet column mode produces acceptable simulation of the nonlinear response that is observed in experiments. However, the sensitivity of the response is sharper than expected.
Various strategies are adapted and implemented for real-time estimation of the flow state from near-field pressure information. These are assessed using the numerical database of the low Reynolds number Mach 0.9 jet. The most useful strategy is the linear time invariant filter employing a linearized version of the dynamic model developed for the unforced jet. This is shown to be more accurate than the more common stochastic estimation techniques, while requiring minimal processing resources.
The actual design of the feedback laws in this very challenging problem remains an open question. The possible directions to take in addressing this in the future are discussed.