This investigation presents a unique and elaborate set of experiments relating the generation of noise to the evolution of large-scale turbulence structures within an ideally expanded, Mach 1.28, high-Reynolds-number (1.03 × 10 6) jet. The results appear to indicate many similarities between the noise generation processes of highspeed low-Reynolds-number and high-speed high-Reynolds-number jets. Similar to the rapid changes observed in the region of noise generation in low-Reynoldsnumber jets in previous experimental and computational work, a series of robust flow features formed approximately one convective time scale before noise emission and then rapidly disintegrated shortly before the estimated moment of noise emission. Coincident with the disintegration, a positive image intensity fluctuation formed at the jet centreline in a region that is immediately past the end of the potential core. This indicates mixed fluid had reached the jet core. These results are consistent with the formation of large-scale structures within the shear layer, which entrain ambient air into the jet, and their eventual interaction and disintegration apparently result in noise generation. These results are quite different from the evolution of the jet during prolonged periods that lacked significant sound emission. The observations presented in this work were made through the use of well-established techniques that were brought together in an unconventional fashion. The sources of large-amplitude sound waves were estimated in time and three-dimensional space using a novel microphone array/beamforming algorithm while the noise-generation region of the mixing layer was simultaneously visualized on two orthogonal planes (one of which was temporally resolved). The flow images were conditionally sampled based on whether or not a sound wave was created within the region of the flow while it was being imaged and a series of images was compiled that was roughly phase-locked onto the moment of sound emission. Another set of images was gathered based on a lack of sound waves reaching the microphone array over several convective time scales. Proper orthogonal decomposition (POD) was then used to create a basis for the flow images and this basis was used to reconstruct the evolution of the jet.

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.

This work is focused on the development of a reduced-order model based on experimental data for the design of feedback control for subsonic cavity flows. The model is derived by applying the proper orthogonal decomposition (POD) in conjunction with the Galerkin projection of the Navier-Stokes equations onto the resulting spatial eigenfunctions. The experimental data consist of sets of 1000 simultaneous particle image velocimetry (PIV) images and surface pressure measurements taken in the Gas Dynamics and Turbulent Laboratory (GDTL) subsonic cavity flow facility at the Ohio State University. Models are derived for various individual flow conditions as well as for their combinations. The POD modes of the combined cases show some of the characteristics of the sets used. Flow reconstructions with 30 modes show good agreement with experimental PIV data. For control design, four modes capture the main features of the flow. The reduced-order model consists of a system of nonlinear ordinary differential equations for the modal amplitudes where the control input appears explicitly. Linear and quadratic stochastic estimation methods are used for real-time estimation of the modal amplitudes from real-time surface pressure measurements.

One of the current three main thrust areas of the Collaborative Center of Control Science (CCCS) at The Ohio State University is feedback control of aerodynamic flows. Synergistic capabilities of the flow control team include all of the required multidisciplinary areas of flow simulations, low-dimensional and reduced-order modeling, controller design, and experimental integration and implementation of the components along with actuators and sensors. The initial application chosen for study is closed-loop control of shallow subsonic cavity flows. We have made significant progress in the development of various components necessary for reduced-order model based control strategy, which will be presented and discussed in this paper. Stochastic estimation was used to show that surface pressure measurements along with the reduced-order model based on flow-field variables can be used for closed-loop control. Linear controllers such as H ∞ , Smith predictor, and PID were implemented experimentally with various degrees of success. The results showed limitations of linear controllers for cavity flow with inherent nonlinear dynamics. Detailed experimental work further explored the physics and showed the highly non-linear nature of the cavity flow and the effects of forcing on the flow structure.

Results are presented from the application of the snapshot proper orthogonal decomposition (POD) method to a spatiotemporal ow eld generated from large eddy simulations (LES) of a Mach 1.4 ideally expanded jet. This is part of ongoing research in the development and use of the POD method in conjunction with advanced laser-based optical measurements in high-speed ows. The POD application goal is twofold: to extract dynamically signi cant information on the large-scale coherent structures in a high-speed jet and to facilitate low-dimensional modeling of the jet. It was found that the spatial eigenmodes obtained using weakly correlated snapshots, but spanning tens of convective timescale and uncorrelated snapshots, are similar. It was also found that a shortduration temporally resolved LES data (simulating data obtainable from pulse burst laser-based measurements) could be used to calculate the time evolution coef cients of the eigenmodes. The use of a few modes (namely, 12) was suf cient for a reasonable reconstruction of the spatiotemporal ow eld. The use of POD with a vector norm instead of a scalar norm did reduce the energy captured in the rst few modes and also changed their rank order, but did not substantially alter the reconstructed ow. In the early jet development region, the rst and dominant mode was found to be axisymmetric, followed by either another axisymmetric or asymmetric (probably helical) mode, whereas higher modes in this region and all of the modes farther downstream were more complex and threedimensional. The POD modes and their temporal coef cients obtained at various streamwise locations suggest that the large-scale jet structures undergo a process of disorganization near the end of potential core, followed by reorganization farther downstream.