Julie M. Ausseur

Proportional closed-loop feedback control of flow separation

The aim of this experimental study is the implementation of a practical and efficient closed-loop feedback control of the turbulent flow over a NACA-4412 airfoil equipped with leading-edge zero-net-mass-flux actuators. By using prior computation of correlations between particle image velocimetry data and multiple surface pressure measurements, real-time instantaneous low-dimensional estimates of the velocity field over the wing are then computed from the unsteady surface pressure. From such estimates, a direct knowledge of the state of the flow above the airfoil is obtained (i.e., attached, incipient separation, or fully separated flow). We first show the effectiveness of the low-dimensional modeling approach in extracting and estimating the underlying large-scale structures in a turbulent flow, using the proper orthogonal decomposition and the modified linear/quadratic stochastic measurements. We then show how such an approach is used successfully in a simple, but practical, proportional feedback loop to delay the separation of the flow over the wing at high angles of attack. The benefits of closed-loop vs open-loop control are then discussed. These fundamental results validate the use of low-dimensional modeling techniques for further, more sophisticated, closed-loop feedback control algorithms.

Experimental Development of a Reduced-Order Model for Flow Separation Control

Practical methods to enable control of turbulent ∞ows in a closed-loop sense are developed with a direct application in this case to ∞ow separation control over an airfoil. The tools used to reduce the dimension and complexity of the problems are based on the Proper Orthogonal Decomposition (POD) and on measurement algorithms derived from the Linear Stochastic Estimation (LSE). Signiflcant progress has been made in the measurement techniques that enable a practical estimation of an entire velocity fleld from surface pressure measurements. This in turn, permits a more accurate representation of the system when developing dynamical systems based on experimental data. The ultimate goal is to derive a plant that accurately represents the ∞ow dynamics and that contains an actuation input explicitly.

Controller development for closed-loop feedback control of flows

The aim of this study is to implement a closed-loop feedback control with a modeled controller of the flow over a NACA-4412 airfoil equipped with leading-edge zero net-mass actuators. We showed at the AIAA 2004 Portland meeting how low-dimensional methods can be effective for smart flow control. A first simple proportional feedback method was a crucial starting point for verifying the applicability of such low-dimensional methods to, not only control of flow separation over a wing, but to flow control in general. These methods based on the Proper Orthogonal Decomposition (POD) and modified Linear Stochastic Measurement (mLSM) techniques have already shown effective in extracting, estimating and representing the most energetic features of turbulent flows but the proportional feedback control showed that these features were great candidates for applied flow control. Using only real-time measurements of unsteady pressure along the chord of the airfoil, we are able to spatially estimate the flow field above the wing at all times and sense the incipient separation. For a better understanding of the actuation effect on the flow over the NACA-4412 airfoil, Particle Image Velocimetry (PIV) measurements in a wide window above the airfoil were taken. A higher order estimation, the modified Quadratic Stochastic Estimation (mQSM) is performed here and shows more effective in representing the coherent structures in the flow. By then solving a system of ordinary differential equations based on learning samples of the estimated POD coefficients and through Low-Order Dynamical Systems (LODS) development, we are able to obtain an estimate of the evolution equation of the flow. A novel way of decomposing the velocity field enables us to explicitly include the effect of the actuation in the evolution equation of the flow above the NACA-4412 airfoil for controller development.

Towards Closed -Loop Feedback Control of the Flow over NACA -4412 Airfoil

We are developing methods to predict the dynamics of the flow field above a NACA -4412 airfoil using real -time measurements of the pressure from the surface of the airfoil only. Through Proper Orthogonal Decomposition ( POD) and modified Linear Stochastic Estimation ( mLSE) low -dimensional techniques, these pressure measurements are coupled to Particle Image Ve locimetry ( PIV) data of the flow to estimate the time dependent coefficients describing the flow. By solving a system of ODEs based on these coefficients, we are able to obtain an estimate of the evolution equation of the flow. This low -dimensional estimat ed plant will be used to explore different Proportional Integral & Derivative (PID) control parameters and will enable us to implement a controller of the flow state above the airfoil using leading edge zero net -mass flow actuators. In an open -loop investi gation, we were able, with the actuation, to keep the flow attached or in an incipient state, well over the stall angle of the uncontrolled airfoil. Furthermore, the experimental set up has been specifically designed to conduct closed -loop control while in cluding dynamic pitching motion of the airfoil. Results of the open -loop control, the application of the POD/mLSE estimation procedure and the prediction capability of the model ODEs will be presented. In addition, we will discuss the use of these tools fo r feedback control.

Flow separation control using a convection based POD approach

The standard Proper Orthogonal Decomposition (POD) is an optimal tool to extract the energy-containing structures from a turbulent flow field. Some POD applications involve more than the structure identification process, and use the resulting eigenfunctions as a subspace onto which the flow state equations are projected, thus creating a low-dimensional model for the system under study. For these more elaborate applications, an increasing number of which are in the field of flow control, this low-dimensional plant is expected to represent the flow dynamics as accurately as possible. In this work, which ultimately intends to control the flow separation over an airfoil using a dynamical model of the flow, we introduce a variation to the POD formulation that we will refer to as the convection POD or cPOD. This formulation is developed using the non-linear convection terms of the Navier-Stokes equations to build a new kernel, thus producing a subspace knowledgeable about the dynamical realizations in the flow. We show that the convection POD succeeds in capturing the dynamical features of the flow more effectively than the standard formulation. It is found that the eigenfunctions now reveal physical structures in the flow field as opposed to patterns of highest energy concentration. Possible improvements in flow control applications and potential difficulties associated with this method are also discussed.

Estimation techniques in a turbulent flow field

Part of our continuous efiorts to implement an efiective closed-loop feedback control of the ∞ow over a NACA 4412 airfoil is the obtention of an accurate estimate of the actual ∞ow state. An elaborate controller combines both prediction and measurement techniques to obtain a precise estimation of the control variable. In this paper we focus on the measurement process. We flrst present the difierent candidates for the control variable, and describe the low-dimensional techniques employed. We then focus on the estimation methods that will be incorporated in the controller in order to access the state variable from the pressure real-time measurements. The investigation of the dynamics in the ∞ow fleld and the correlations between the variables at stake reveal the beneflts brought by a spectral estimation approach.

Interactions of Zero Net-Mass Flow Actuators the Flow over NACA 4412 Foils

An investigation of the global effects of the actuation system on the flow field over the NACA-4412 foils has been done as part of our effort to implement real time closed loop separation control using zero net-mass flow actuators. Our approach involves an application to the NACA-4412 foils of the method develop by Honohan et al. (2003) in which Particle Image Velocimetry (PIV) data coupled with the Reynolds Averaged Navier Stokes (RANS) equations to obtain the effect of the flow control actuation on the averaged pressure field. We have demonstrated (Andino et al.2005) the utility of this approach on the NACA-4412 hydrofoil to help us understand the global effects of flow control. A major effect of the actuation on the mean pressure field was backed out from the PIV/RANS approach.

Low-Dimensional Tools for Closed-Loop Flow-Control in High Reynolds Number Turbulent Flows

A summary of recent experimental research efforts at Syracuse University aimed at active flow control is presented with emphasis placed on the development of low-dimensional tools to facilitate closed-loop control. Results indicate that the near-field pressure in a Mach 0.85 high Reynolds number jet is low dimensional and it is primarily the azimuthal near-field pressure mode 0 that correlates with the acoustic field. The turbulent velocity field in the high-speed jet can also be estimated from the near-field pressure, and is used herein to predict the far-field acoustics. Tools being developed to improve recent successful, high Reynolds number, closed-loop flow control in a NACA 4412 airfoil are also discussed. Together, these results set the framework for active flow control in the high-speed jet with the goal of reducing jet noise.

Low-Order Models of the Fluctuating Wall Pressure in an Incompressible Turbulent Impinging Jet

The ∞uctuating wall pressure fleld measured simultaneously at 137 points in an impinging jet with ReD = 23;000 and a nozzle-to-plate spacing of two diameters. A previous time averaged azimuthal decomposition 1 indicated that the ∞uctuating pressure fleld could be accurately described using few azimuthal modes, indicating this ∞ow is an excellent candidate for a Low-Order Dynamical Systems (LODS) model. The present model was developed using a method similar as Ricaud, 2 whereby a general cubic order system of equations is flt to the experimentally determined Fourier coe‐cients. A LODS model developed using only azimuthal modes 0, 1 and 2 was able to reasonably accurately capture the behaviour of the ∞uctuating pressure fleld at r=D = 1:5. Downstream at r=D = 2:0, where the pressure fleld is more three-dimensional, the addition of azimuthal mode 3 is required to produce a stable system of equations, that again, reasonably captures the dynamics of the ∞uctuating pressure fleld. The success of this technique here, suggests that it may prove useful in high speed ∞ow control applications where some degree of predictive ability is required.