Marco Debiasi

Feedback control of subsonic cavity flows using reduced-order models

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 10 5 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 uses 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 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.

Directional Suppression of Noise from a High-Speed Jet

Experiments demonstrate directional suppression of noise from a high-speed jet using an asymmetric parallel secondary stream. The secondary stream attenuates Mach wave radiation in the lower hemisphere of the acoustic far eeld, leaving unaltered the upward-propagated Mach waves. An eccentric nozzle arrangement with a Mach 1.5, 700-m/s inner stream and a Mach 1.0, 360-m/s outer stream produces noise reduction superior to that from concentric arrangements or from the fully mixed equivalent jet. The angle of peak perceived noise shifts from the aft quadrant to the lateral direction. The beneet of the eccentric arrangement is attributed to its shorter potential core relative to a concentric jet. The experiments also reveal emission of strong crackle from the untreated jet, a noise component arising from the nonlinearity of Mach waves. The secondary eow suppresses crackle.

Noise Measurements in Supersonic Jets Treated with the Mach Wave Elimination Method

We report noise measurements for perfectly expanded coaxial jets composed of a supersonic primary stream at velocity of 920 m/s and a coflow stream at conditions designed to prevent formation of Mach waves. Both the primary and secondary streams consisted of helium-air mixtures to simulate approximately the conditions of hot flows, The resulting sound field was compared to that emitted by a single jet at the conditions of the primary stream. Overall sound pressure levels (OASPL) and noise spectra were obtained at many radial and azimuthal positions around the jet exit. Equal-thrust comparisons were made by using geometric scaling. At equal thrust, Mach wave elimination reduced the near-field OASPL by 11 dB and the far-field OASPL by 5 dB. The mid-to-high-frequency region of the spectrum, which is most pertinent to aircraft noise, was reduced by 20 dB in the near field and by 9 dB in the far field. It is shown that Mach waves account for at least 85 % of the sound field most relevant to aircraft noise.

Logic-based active control of subsonic cavity flow resonance

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. I. Introduction A PPLICATION of closed-loop control in fluid dynamics is by its nature a challenging and fascinating problem. Although many significant results have been obtained with open-loop flow control, this technique lacks the responsiveness or the flexibility needed for application in dynamic flight environments. In contrast, closed-loop flow control, although in its infancy, appears to be the ideal technique for the successful management of flow in many applications due to its adaptability to variable conditions and to its potential for significantly reducing the power required for controlling the flow. Fo re xample, Cattafesta et al. 1 found that closed-loop control of cavity tones requires an order-of-magnitude less power than open-loop control. The results presented here are part of a larger multidisciplinary effort to develop tools and methodologies that can apply closed-loop aerodynamic flow control for manipulating the flow over maneuvering air vehicles. The first step was to select a particular flowfield relevant to Air Force applications and to utilize it in the development of various components of closed-loop flow control techniques. The case study chosen is the control of shallow cavity flow pressure fluctuations that are characterized by a strong resonance produced by a natural feedback mechanism similar to that occurring in other flows with self-sustained oscillations (e.g., impinging jet, screeching jet). In all of these cases, shear layer structures impacting a discontinuity or obstacle in the flow (e.g., the cavity trailing edge) scatter acoustic waves that propagate upstream and reach the shear layer receptivity region where they tune and enhance the development and growth of shear layer structures. In the case of flow over a weapon bay cavity, these fluctuations can lead to structural damage to the air vehicle or to the stores carried within the bay. Rossiter 2 first developed an empirical formula for predicting the cavity flow resonance frequencies, today referred to as Rossiter frequencies or modes. He also investigated the concept of a dominant mode of oscillation. Later Rockwell and Naudascher 3 ob

Exploring strategies for closed-loop cavity flow control

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.

Experimental study of linear closed-loop control of subsonic cavity flow

A study is presented of the modeling and implementation of different concepts for linear feedback control of a single-mode resonance shallow cavity flow. When a physics-based linear model is used for cavity pressure oscillations, an H ∞ controller was designed and tested experimentally. It significantly reduced the main Rossiter mode for which it was designed, while leading to strong oscillations at other Rossiter modes. Other linear control methods such as Smith predictor controller and proportional integral derivative (PID) controller exhibited similar results. The ineffectiveness of using fixed linear models in the design of controllers for the cavity flows is discussed. A modification of the PID design produced a parallel-proportional with time-delay controller that remedied this problem by placing zeros at the frequencies corresponding to other resonance states. Interestingly, it was observed that introducing the same zero to the H ∞ controller can also successfully avoid the strong oscillations at other Rossiter modes otherwise observed in the single-mode-based design. The parallel-proportional with time-delay controller was compared to a very effective open-loop method for reducing cavity resonance and exhibited superior robustness with respect to departure of the Mach number from the design conditions. An interpretation is presented for the physical mechanisms by which the open-loop forcing and the parallel-proportional with time-delay controllers reduce the cavity flow noise. The results support the idea that both controls induce in the system a rapid switching between modes competing for the available energy that can be extracted from the mean flow.

Development and Implementation of an Experimental-Based Reduced-Order Model for Feedback Control of Subsonic Cavity Flows

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.

Feedback Control of Cavity Flow Using Experimental Based Reduced Order Model

We present preliminary results on subsonic cavity flow control using reduced-order model based feedback control derived from experimental measurements. The reduced-order model was developed using the Proper Orthogonal Decomposition of PIV results in conjunction with the Galerkin projection of the Navier-Stokes equations onto the resulting spatial eigenfunctions. The stochastic estimation method was used for real-time estimate of the model time coefficients from dynamic surface pressure measurements. Equilibrium analysis led to the linearization of the reduced-order model around the equilibrium point and a model for controller design was obtained by shifting the origin of the coordinates to the equilibrium point. A linear-quadratic optimal controller was then designed and tested in the experiments. The results obtained are very promising and show that control is capable of reducing the cavity flow resonance not only at the Mach 0.3 flow, for which the reducedorder model was specifically derived, but also at other flows with some variation of the Mach number. These preliminary results indicate that the control switches the flow from a single mode resonance to a multi-mode resonance.

Control of Subsonic Cavity Flows by Neural Networks - Analytical Models and Experimental Validation

Flow control is attracting an increasing attention of researchers from a wide spectrum of specialties because of its interdisciplinary nature and the associated challenges. One of the main goals of The Collaborative Center of Control Science at The Ohio State University is to bring together researchers from different disciplines to advance the science and technology of flow control. This paper approaches the control of subsonic cavity flow, a study case we have selected, from a computational intelligence point of view, and offers a solution that displays an interconnected neural architecture. The structures of identification and control, together with the experimental implementation are discussed. The model and the controller have very simple structural configurations indicating that a significant saving on computation is possible. Experimental testing of a neural emulator and of a directlysynthesized neurocontroller indicates that the emulator can accurately reproduce a reference signal measured in the cavity floor under different operating conditions. Based on preliminary results, the neurocontroller appears to be marginally effective and produces spectral peak reductions analogous to those previously observed by the authors using linearcontrol techniques. The current research will continue to improve the capability of the neural emulator and of the neurocontroller.

Closed-Loop Active Flow Control - A Collaborative Approach

The Collaborative Center of Control Science (CCCS) at The Ohio State University was founded very recently with funding from the Air Force Research Laboratory to conduct multidisciplinary research in the area of feedback control, with applications such as cooperative control of unmanned air vehicles (UAVs), guidance and control of hypersonic vehicles, and closed-loop active flow control. The last topic is the subject of this paper. The goal of this effort is to develop tools and methodologies for the use of closedloop aerodynamic flow control to manipulate the flow over maneuvering air vehicles and ultimately to control the maneuvers of the vehicles themselves. It is well known in the scientific community that this is a challenging task and requires expertise in flow simulation, low dimensional modeling of the flow, controller design, and experimental integration and implementation of these components along with actuators and sensors. The CCCS flow control team possesses synergistic capabilities in all these areas, and all parties have been intimately involved in the project from the beginning, a radical departure from the traditional approach whereby an experiment is designed and constructed, data are collected, a model is developed, and a control law is designed, i.e. the system is assembled for validation in a sequential fashion. The first problem chosen for study, control of the noise created by a shallow cavity placed in a flow, has specific relevance to the needs of the Air Force. For example, significant pressure fluctuations in an aircraft weapon bay can lead to structural damage to the air vehicle, to the stores carried in the cavity, and especially to the electronics carried onboard the stores. The team has been working together for a relatively short period of time. Nevertheless, significant progress has been made in the development of various components of the closed-loop cavity flow control problem. The paper will present and discuss the progress made to date and future plans.