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Flow control of weakly non-parallel flows: application to trailing vortices. (English) Zbl 1383.76072
Summary: A general formulation is proposed to control the integral amplification factor of harmonic disturbances in weakly non-parallel amplifier flows. The sensitivity of the local spatial stability spectrum to a base-flow modification is first determined, generalizing the results of A. Bottaro et al. [ibid. 476, 293–302 (2003; Zbl 1041.76029)]. This result is then used to evaluate the sensitivity of the overall spatial growth to a modification of the inlet flow condition. This formalism is applied to a non-parallel Batchelor vortex, which is a well-known model for trailing vortices generated by a lifting wing. The resulting sensitivity map indicates the optimal modification of the inlet flow condition enabling the stabilization of the helical modes. It is shown that the control, formulated using a single linearization of the flow dynamics carried out on the uncontrolled configuration, successfully reduces the total spatial amplification of all convectively unstable disturbances.
76B47 Vortex flows for incompressible inviscid fluids
76B75 Flow control and optimization for incompressible inviscid fluids
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