Feedbacks for Destabilizing Fluid Flows and Stabilizing Solid Propellants

Prof. Miroslav Krstic, Department of Mechanical and Aerospace Engineering, University of California, San Diego

We present results for channel and pipe flows that demonstrate the potential of feedback control for enhancing turbulence and mixing. These controls employ sensing and actuation only at the walls and are designed using Lyapunov synthesis. They achieve, for example, the increase in the flow's turbulent kinetic energy that corresponds to doubling the Reynolds number without actually increasing the mean velocity of the flow. The control kinetic energy spent is only a fraction of a percent of the kinetic energy added to the flow. The reason for this, as recently elucidated by George Haller through analysis and numerical experiments, are that the control does not attempt to override the coherent structures in the open-loop flow, but instead just enlarges and intensifies the open-loop structures, making them penetrate deeper into the flow domain. Another reason is that the controller actually represents an H-infinity worst-case feedback disturbance with respect to a differential game where the control is trying to maximize enstrophy.

The first part of the talk will be dedicated to the problem of stabilizing a model of a thermal instability in an end burning solid propellant rocket. The model is nonlinear and tractable by a nontrivial extension of backstepping where the source of instability, a nonlinear boundary condition on the burning end, cannot be altered by feedback.