Development, experimental implementation, and the results of reduced-order model based feedback control of subsonic shallow cavity flows are presented and discussed. Particle image velocimetry (PIV) data and the proper orthogonal decomposition (POD) technique are used to extract the most energetic flow features or POD eigenmodes. The Galerkin projection of the Navier–Stokes equations onto these modes is used to derive a set of nonlinear ordinary differential equations, which govern the time evolution of the eigenmodes, for the controller design. Stochastic estimation is used to correlate surface pressure data with flow-field data and dynamic surface pressure measurements are used to estimate the state of the flow. Five sets of PIV snapshots of a Mach 0.3 cavity flow with a Reynolds number of 105 based on the cavity depth are used to derive five different reduced-order models for the controller design. One model uses only the snapshots from the baseline (unforced) flow while the other four models each use snapshots from the baseline flow combined with snapshots from an open-loop sinusoidal forcing case. Linear-quadratic optimal controllers based on these models are designed to reduce cavity flow resonance and are evaluated experimentally. The results obtained with feedback control show a significant attenuation of the resonant tone and a redistribution of the energy into other modes with smaller energy levels in both the flow and surface pressure spectra. This constitutes a significant improvement in comparison with the results obtained using open-loop forcing. These results affirm that reduced-order model based feedback control represents a formidable alternative to open-loop strategies in cavity flow control problems even in its current state of infancy.

No abstract

We present the results of an experimental investigation for controlling a shallow cavity flow in the Mach number range 0.25-0.5. The flow exhibits the characteristic staging behavior predicted by the semi-empirical Rossiter formula with multiple modes in the Mach number range 0.32-0.38 and a single strong mode in other Mach numbers. A survey of the velocity at the exit of the zero net mass flow compression-driver actuator used for control reveals that its amplitude is frequency dependent and its behavior is little influenced by the main flow. Forcing the Mach 0.3 flow indicated that the actuator has good authority over a large range of frequencies, with reduction of spectral peaks observed at some forcing frequencies. We took advantage of this phenomenon to develop a logicbased controller that searches the frequency space and maintains the optimal forcing frequency for peak reduction at each Mach number. Optimal frequencies and the corresponding reduced resonance have been obtained for all of the flow conditions explored. The physics of optimal frequency forcing as well as some characteristics of the logic-based controller are discussed.

Experimental investigation of wing flexibility on vertical thrust generation and power consumption in hovering condition for a hovering Flapping-Wing Micro Air Vehicle, namely FlowerFly, weighing 14.5 g with a 3 g onboard battery and having four wings with double wing clap-and-fling effects, was conducted for several wing configurations with the same shape, area, and weight. A data acquisition system was set up to simultaneously record aerodynamic forces, electrical power consumption, and wing motions at various flapping frequencies. The forces and power consumption were measured with a loadcell and a custom-made shunt circuit, respectively, and the wing motion was captured by high-speed cameras. The results show a phase delay of the wing tip displacement observed for wings with high flexible leading edge at high frequency, resulting in less vertical thrust produced when compared with the wings with less leading edge flexibility at the same flapping frequency. Positive wing camber was observed during wing flapping motion by arranging the wing supporting ribs. Comparison of thrust-to-power ratios between the wing configurations was undertaken to figure out a wing configuration for high vertical thrust production but less power consumption.

In our recent work we presented preliminary results for subsonic cavity flow control using a reduced-order model based feedback control derived from experimental measurements. The model was developed using the Proper Orthogonal Decomposition of PIV images in conjunction with the Galerkin projection of the Navier-Stokes equations onto the resulting spatial eigenfunctions. A linear-quadratic optimal controller was designed to reduce cavity flow resonance by controlling the time coefficient and tested in the experiments. The stochastic estimation method was used for real-time estimation of the corresponding time coefficients from 4 dynamic surface pressure measurements. The results obtained showed that the controller was capable of reducing the cavity flow resonance at the design Mach 0.3 flow, as well as at other flows with slightly different Mach number. In the present work we present several improvements made to the method. The reduced order model was derived from a larger set of PIV measurements and we used 6 sensors for the stochastic estimation of the instantaneous time coefficients. The reduced order model so obtained shows a better convergence of the time coefficients. This combined with the 6sensor estimation improves the control performance while using a scaling factor closer to the theoretically expected value. The controller also performed better in off design flow conditions.