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Sensitivity analysis and passive control of cylinder flow. (English) Zbl 1165.76012
The results of this investigation suggest that it is possible to control the global stability of a flow past a body by locally introducing artificial disturbances at appropriately predetermined places in the flow domain. The theory developed in the paper is within the scope of linear stability theory. The authors first present a general theoretical formalism enabling to estimate how base-flow modifications may alter the stability properties of flows studied in a global approach of linear stability theory. This also comprises a systematic approach to the passive control of globally unstable flows by the use of small control devices. The investigated base-flow modifications are either arbitrary or specific ones induced by a steady force. Based on this, the notions sensitivity to base-flow modifications and sensitivity to a steady force are introduced and elaborated. These sensitivity analyzes are applied to the unstable global modes responsible for the onset of vortex shedding in the wake of a cylinder for Reynolds numbers in the range \(47\leq Re\leq80\). First, it is demonstrated how the sensitivity to arbitrary base-flow modifications may be used to identify regions and properties of the base flow that contribute to the onset of vortex shedding. Secondly, the sensitivity to a steady force determines the regions of the flow where a steady force acting on the base flow stabilizes the unstable global modes. A local steady force may be created locally by the introduction of a small control cylinder which exerts a force on the base flow opposite to its drag. By means of the sensitivity to a steady force, positions of the control cylinder that stabilize the flow are predicted and compared with experimental results.

MSC:
76D55 Flow control and optimization for incompressible viscous fluids
76D25 Wakes and jets
76E05 Parallel shear flows in hydrodynamic stability
Software:
ARPACK
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