Physics Colloquium: Feedback Flow Control: Towards Practical Applications

Abstract:  We are developing feedback flow control methods based on the use of Proper Orthogonal Decomposition (POD) and Stochastic Measurement (SM) for various flows including; that over a NACA 4412 airfoil, turbulent jets for noise reduction and 3D separated flow control over turrets for improving aero-optics.  The NACA 4412 work, for example, involves using a combination of Particle Image Velocimetry (PIV) and multiple surface pressure measurements, processed through POD/SM algorithm, from which estimates of the velocity field via wall pressure alone are extracted.  From such estimates knowledge of the state of the flow above the airfoil can be obtained (i.e., attached, fully separated or incipiently separated flow).  Integral to the POD/SM algorithm is the measurement estimation of the global POD coefficients.   Over the past 3 years or so we have demonstrated the utility of these time dependent coef-ficients, which are estimated from surface pressure only, for use in a simple proportional feedback loop (as the time series to drive the actuators) to keep the flow attached.  This methodology is critical for implementation of realistic feedback flow control since surface measurements and not inflow measurements are required for most practical applications.  The next step for more elaborate control involves the development of a model of plant for our system.  To do so we are developing a set of ODEs for the POD coefficients from both direct Galerkin projection with computational results as well as through a novel moment method developed at CEAT/LEA in Poitiers France.  The moment method involves training a non-linear system with the same form of non-linear ODE obtained with the Galerkin method but using as input either experimental or computational POD coefficients (here the POD eigenfuctions are projected using the data obtained from either simulation or PIV data).   This provides a
set of time evolution equations for the POD coefficients (our plant) directly without performing the Galerkin projection with the Navier Stokes equations. The results of the simple proportional feedback NACA 4412 experiment will be presented as well as early results on the plant formulation based on POD eigenfunctions.  We will also discuss progress being made on extending such feedback flow control tools to the jet noise problem as well as for 3D separatedflow over the turret for improving aero-optics.