In this talk we assess the efficacy of a zero-net-mass-flux blowing and suction in the form of streamwise traveling waves for transition control in a channel flow. It was recently shown that the net power balance for this type of actuation is always negative if the uncontrolled flow stays laminar. However, we show that a positive net power balance can be achieved when the uncontrolled flow becomes turbulent but the controlled flow stays laminar. Starting from this observation, we develop a framework for selection of traveling wave parameters for control of transition with a positive net power balance. Our model-based approach shows that, relative to the uncontrolled flow, the velocity fluctuations around the upstream traveling waves at best exhibit similar sensitivity to background disturbances. In contrast, the properly designed downstream traveling waves can significantly reduce sensitivity which makes them well-suited for preventing transition. Our theoretical findings are confirmed by direct numerical simulations of the Navier-Stokes (NS) equations which show that a positive net efficiency as large as 25% relative to the uncontrolled turbulent flow can be achieved. This (i) elucidates the predictive power of the developed theoretical framework for model-based vibrational flow control, and (ii) suggests that the linearized NS equations with uncertainty represent an effective control-oriented model for preventing transition.
Mihailo Jovanovic received the Dipl. Ing. and M.S. degrees from the University of Belgrade, Serbia, in 1995 and 1998, respectively, and the Ph.D. degree from the University of California, Santa Barbara, in 2004. He was a Visiting Researcher with the Department of Mechanics, the Royal Institute of Technology, Stockholm, Sweden, from September to December 2004. He joined the University of Minnesota, Minneapolis, as an Assistant Professor of Electrical and Computer Engineering in December 2004. His primary research interests are in modeling, analysis, and control of spatially distributed dynamical systems. He is a member of IEEE, SIAM, and APS and an Associate Editor of the IEEE Control Systems Society Conference Editorial Board. He received a CAREER Award from the National Science Foundation in 2007.
