The objective of the course is to introduce and adapt modern flow control techniques in order to stabilize flow instabilities and therefore delay transition to turbulence. Both open-loop and closed-loop control strategies will be presented.
These issues play a crucial role in both aeronautical and mechanical engineering applications.
Denis Sipp, ONERA/DAFE
- Instabilities and global modes in open shear-flows.
- Open-loop control with adjoint methods: variational formulation, adjoint operators, adjoint global modes, eigenvalue sensitivity.
- Open-loop control with amplitude equations: the forced Van der Pol oscillator, multiple time-scale analysis, compatibility condition, bifurcation analysis in real systems.
- Model reduction with balanced truncation: input/output dynamics, observability and controllability Gramians, Hankel singular-values, balanced basis.
- Closed-loop control with estimator / controller setup: Riccati-based feedback control , full-state information control, partial state information control, estimation and Kalman filtering.
All concepts will be illustrated on cylinder and open-cavity flows.
The students will work on the concepts in class thanks to numerical codes based on FreeFem++ and Matlab.
Requirements : Introduction to hydrodynamic instabilities (MEC631). Fundamental notions of fluid mechanics
Credits ECTS : 3