Abstract

The talk will describe the rational set up of a fundamental flow control problem, where active flow control is used to reduce turbulent skin-friction drag in an indefinite plane channel. The proper way of accounting for the energy cost of the control, as well as the cor- rect objective function in an optimization procedure, will be identified and discussed. The framework builds upon the Constant Power Input (CPI) concept, that we have re- cently introduced as a viable alternative to compare different flows under flow control. With CPI , at statistical equilibrium each flow has the same global energy flux per unit time, hence the same total energy dissipation rate. A new decomposition of the total dissipation is introduced, stemming from an ex- tended Reynolds decomposition, where the mean velocity is split into a laminar com- ponent and a deviation from it. The figure below shows for the most general case the different energy fluxes of Mean Kinetic Energy (MKE) and Turbulent Kinetic Energy (TKE).