Active control of cavity-flow resonances

Feedback control has allowed great preformance improvement in many technical fields such as robotics, aerospace, telecommunication, transportation systems, manufacturing systems, and chemical processes. Recently, various attempts have been made to apply feedback control techniques to aerodynamics. This is very challenging since often flow can not be described by simple models. The Collaborative Center of Control Science at The Ohio State University is contributing to the advancement of the state of the art in this field with a multi-disciplinary effort to develop tools and methodologies for feedback flow control. Initially this is done by choosing as a benchmark problem the control of cavity flow resonance.

To control the cavity flow noise, a two-dimensional synthetic-jet type actuator is used in the cavity-flow facility. This is a powerful loudspeaker connected to a converging cone ending in a slot at the beginning of the cavity. In this arrangement the waves created by the loudspeaker are directed to the position where the vortices are created so to control their formation. More details about the actuator can be found in my publications.

The first attempt to control cavity flow resonance was done by using open-loop forcing. Basically I explored the effect of actuation at different frequencies and intensities. This yelded some very interesting results. For instance, actuation at 3250 Hz reduced the noise by 18 dB without introducing much noise of its own, Fig. 1 . This remarkable finding, observed also for actuation at about 3900 Hz (not presented here), inspired the design of a simple logic-based control process that automatically searches for optimal actuation conditions for reducing cavity flow resonance. This technique, which is described in more details in AIAA Journal Vol. 42 No. 9, performed well in the experiments as it was able to find and maintain forcing frequencies that reduce cavity flow resonance in the entire range of Mach number explored, Fig. 2. Furthermore, it proved to be a powerful tool for extracting valuable information about the effect of control in a large range of forcing conditions.

 Mach 0.30 with OpFF  OpFF effect
Figure 1: Spectra of Mach 0.30 flow without
control (red) and with actuation at 3250 Hz
Figure 2: Plots of maximum spectral peak
between Mach 0.25 and 0.5: red is without forcing,
green is with forcing at frequencies and intensities
for reduction of noise.

With the colleagues of CCCS I also studied and tested different linear controls of the cavity flows resonance. In general these controls significantly reduce the noise at the Rossiter frequency for which they are designed, but they lead to strong noise at other frequencies (AIAA 2004-0573). A modification of the PID linear control produced a parallel-proportional (PP) with time delay control that remedied this problem, Fig. 3. This method is as effective as the open-loop method described above, but it it is superior to it since it requires less control power and is more "robust" since it works well even if small changes occur to the air flow (as shown, for instance, in Fig. 4 for the flow at Mach 0.27; see also AIAA 2004-2123).

 Mach 0.30 with PP  Mach 0.27 with PP
Figure 3: Spectra of Mach 0.30 flow without
control (red) and with PP control (blue).
Figure 4: Spectra of Mach 0.27 flow without
control (red) and with PP control (blue).

A the 35th AIAA Fluid Dynamics Conference and Exhibit (2005) I presented some preliminary results on a significant advancement by using a state feedback controller based on a reduced order model of the cavity flow (see AIAA 2005-5269 for more details). The method involves several successive steps.
First, Particle Image Velocimetry (PIV, see Fig. 5) is used to capture the flow over the cavity. Many of these images are processed with the Proper Orthogonal Decomposition (POD) method to approximate the temporal-spatial evolution of the flow as a combination of spatial modes (POD modes) whith amplitude modulated in time by coefficients (time coefficients). The flow quantities (for instance, the velocity) obtained using this approximation are then introduced in the Navier-Stokes equations, i.e. the equations most generally used to describe the flow phenomena. These represent a good but very complex model of the flow that is not amiable to use for control. However, by projecting onto the POD modes what obtained with the previous steps, a simpler model is obtained that can be used to design a controller. For doing that one actually needs also to know the updated values of the time coefficients and this is done by using stochastic estimation to estimate them from real-time pressure measurements in different locations on the side wall of the cavity (see Fig. 6).

 vector field of Mach 0.30  Pressure transducers
Figure 5: Vector field superimposed on an
absolute velocity contour of Mach 0.30 flow.
Figure 6: Pressure transducers on the side
wall of the cavity.

Once obtained with the steps above a workable model of the cavity flow, this can be further simplified by linearizing it around its equilibrium point (corresponding to the mean flow, a quieter state than the resonant one) and by shifting the origin of the coordinates to this equilibrium point. Then a linear-quadratic (LQ) state feedback controller is designed to bring and keep the system to the equilibrium point (Fig. 7).

The results obtained by testing experimentally the procedure above indicate that the controller significantly reduces the resonance peak of the Mach 0.3 flow for which it was designed, see Fig. 8. The controller seems to be quite robust, as it can control the flow with some variations in the flow Mach number. While in term of sheer noise reduction this more sophisticated method seems somewhat less effective than the ones described above, it actually represents a big leap forward as it is based on a model of the flow and it enables the use of modern control theory techniques to a higher degree.

 LQ state feedback controller  Mach 0.30 with LQ
Figure 7: Diagram of the closed loop system
with linear quadratic state feedback control.
Figure 8: Spectra of Mach 0.30 flow without
control (red) and with linear quadratic control

I am confident that by improving the model and the controller, we will be able at least to match the previous results and to define the path for further progress in flow control.
Stay tuned and visit again this page in the future for an update about this ground-breaking research.

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© Copyright 2005 Marco Debiasi
Last modified on: 21 February 2011