Identification and Control of the Jet in Crossflow
- Author(s): Hendrickson, Cory Scott
- Advisor(s): M'Closkey, Robert T
- et al.
The research in this dissertation explores active control of a jet injected into quiescent surrounding or into a crossflow, a flowfield also known as the transverse jet. Periodic acoustic actuation is used to perturb the temporal jet injection profile about a mean in order to enhance important characteristics of the flow, such as mixing and penetration of the jet into the crossflow. In practice, nonlinear actuation system dynamics make it difficult to shape the injection profile to match a periodic reference. Discrete sinusoidal inputs necessary for periodic reference tracking produce harmonics that fall directly on the neighboring harmonic frequencies of the reference.
At low forcing amplitudes, approximately less than 0.5m/s RMS, a feedback controller designed from a linear model of the actuation system compensates the coupling between harmonics. A modulated-demodulated controller with feedback from a hotwire placed at the jet exit tracks the first N Fourier coefficients of the reference that fall within the actuation bandwidth. A fundamental improvement to modulated-demodulated control, dynamic phase compensation in place of static phase compensation, is presented to reduce sensitivity function peaking in the neighborhood of the frequencies targeted for rejection or tracking. Above 0.5m/s RMS, however, the harmonic coupling destabilizes modulated-demodulated control designed from a linear model of the actuator dynamics.
An alternative approach creates a stabilizing feedback control based on a multi-input, multi-output (MIMO) empirical model of the harmonic coupling. Transforming the system into baseband coordinates by demodulating the velocity measurement at the harmonic frequencies of the reference waveform simplifies the model to the point the harmonic coupling can be reasonably modeled as a linear MIMO gain. The static model accurately captures the relationship between each harmonic frequency in the neighborhood of an operating point close to a desired reference. The stable feedback loop asymptotically drives the jet velocity to its reference.
This control method is applied to the equidensity jet in crossflow to track pulse-like references at jet to crossflow velocity ratios of R=6.4 and R=2.2. The closed-loop waveforms are symmetric with little ringing and have sharp transitions between the low and high velocity regions of the pulse. Initial experiments with planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV) flow diagnostics are also presented. These results show the pulsed jet in crossflow with optimized temporal pulse widths increases the jet spread compared to the unforced and sinusoidally forced jet in crossflow. Additionally, the pulsed jets increase the centerline scalar concentration decay in the near field but become approximately equal with the unforced jet in the far field.