Flow control design inspired by linear stability analysis

Abstract

In the recent literature, a growing number of research papers have been dedicated to applying the techniques of global stability and sensitivity analysis to the design of flow controls. The controls that are designed in this way are mainly passive or open-loop controls. Among those, we consider here controls that are aimed at linearly stabilizing flow configurations which would be otherwise globally unstable. In particular, a review of the literature on flow controls designed on the basis of stability and sensitivity analysis is presented. The mentioned methods can be rigorously applied to relatively simple flow regimes, typically observed at low values of the Reynolds number. In this respect, the recent literature also demonstrates a large interest in the application of the same methods for the control of coherent large-scale flow structures in turbulent flows, as, for instance, the quasiperiodic shedding of vortices in turbulent wakes. The papers dedicated to this subject are also reviewed here. Finally, all the described methods imply the solution of eigenvalue problems which are at the state-of-the-art for computational complexity. On the one hand, there are attempts to reduce the complexity of the involved computational problems by applying local stability analysis, and some examples are illustrated. On the other hand, recent advances in numerical methods, also concisely reviewed here, allow the manipulation of large eigenvalue problems and greatly simplify the development of numerical tools for stability and sensitivity analysis of complex flow models, often built using existing fluid dynamics codes.